Why we don't normally teach chord, versine, coversine, haversine, exsecant, excosecant any more?
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10
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It seems that the following functions are not only excluded from a course in trigonometry, they are almost never taught in any course:
- Chord
- Versine
- Coversine
- Haversine
- Exsecant
- Excosecant
I could have asked the same question with the title "why have these functions lost their popularity" at math.stackexchange, but I fear that they will consider this question as "opinion-based".
trigonometry
asked 16 hours ago
Zuriel
611411
|
show 7 more comments
up vote
10
down vote
favorite
It seems that the following functions are not only excluded from a course in trigonometry, they are almost never taught in any course:
- Chord
- Versine
- Coversine
- Haversine
- Exsecant
- Excosecant
I could have asked the same question with the title "why have these functions lost their popularity" at math.stackexchange, but I fear that they will consider this question as "opinion-based".
trigonometry
asked 16 hours ago
Zuriel
611411
4
These things were useful when you had to look everything up in tables. But nowadays, with hand-held scientific calculators, we do not need them.
– Gerald Edgar
16 hours ago
2
I don't teach these functions because I don't know what they are. I've heard of only half of them, but even for that half I'd need to look up their definitions. Students can look them up as well as I can.
– Andreas Blass
14 hours ago
2
On the one hand, you could get the answer from Wikipedia articles that you linked. On another hand, I learned something new, so thanks. Not sure why you included chord, which is not a trigonometric function, and is taught at school. As for "popular" functions, sine is useful when studying waves, cosine is useful to find a projection of a force, and tangent is the slope of tangent line, that is, a derivative. I guess finding a trajectory of a ballistic missile is more important nowadays than finding position of a brigantine.
– Rusty Core
13 hours ago
1
@PeterTaylor Thanks, fixed it
– Chris Cunningham
12 hours ago
2
Even with the calculators, I bet almost all students don't even know what a versine is when they see it. --- I don't understand the reasoning behind of this statement. For example, even with calculators, I bet almost all students don't know what a vulgar fraction is when they see it. In fact, even with calculators, I bet almost all students don't know what a syntopogenic space is when they see it. My point is that I don't understand why one would expect students who have a calculator to be more likely to know what a versine is.
– Dave L Renfro
10 hours ago
|
show 7 more comments
up vote
10
down vote
favorite
up vote
10
down vote
favorite
It seems that the following functions are not only excluded from a course in trigonometry, they are almost never taught in any course:
- Chord
- Versine
- Coversine
- Haversine
- Exsecant
- Excosecant
I could have asked the same question with the title "why have these functions lost their popularity" at math.stackexchange, but I fear that they will consider this question as "opinion-based".
trigonometry
asked 16 hours ago
Zuriel
611411
It seems that the following functions are not only excluded from a course in trigonometry, they are almost never taught in any course:
- Chord
- Versine
- Coversine
- Haversine
- Exsecant
- Excosecant
I could have asked the same question with the title "why have these functions lost their popularity" at math.stackexchange, but I fear that they will consider this question as "opinion-based".
trigonometry
trigonometry
asked 16 hours ago
Zuriel
611411
asked 16 hours ago
Zuriel
611411
edited 11 hours ago
asked 16 hours ago
Zuriel
611411
asked 16 hours ago
Zuriel
611411
asked 16 hours ago
Zuriel
611411
611411
4
These things were useful when you had to look everything up in tables. But nowadays, with hand-held scientific calculators, we do not need them.
– Gerald Edgar
16 hours ago
2
I don't teach these functions because I don't know what they are. I've heard of only half of them, but even for that half I'd need to look up their definitions. Students can look them up as well as I can.
– Andreas Blass
14 hours ago
2
On the one hand, you could get the answer from Wikipedia articles that you linked. On another hand, I learned something new, so thanks. Not sure why you included chord, which is not a trigonometric function, and is taught at school. As for "popular" functions, sine is useful when studying waves, cosine is useful to find a projection of a force, and tangent is the slope of tangent line, that is, a derivative. I guess finding a trajectory of a ballistic missile is more important nowadays than finding position of a brigantine.
– Rusty Core
13 hours ago
1
@PeterTaylor Thanks, fixed it
– Chris Cunningham
12 hours ago
2
Even with the calculators, I bet almost all students don't even know what a versine is when they see it. --- I don't understand the reasoning behind of this statement. For example, even with calculators, I bet almost all students don't know what a vulgar fraction is when they see it. In fact, even with calculators, I bet almost all students don't know what a syntopogenic space is when they see it. My point is that I don't understand why one would expect students who have a calculator to be more likely to know what a versine is.
– Dave L Renfro
10 hours ago
|
show 7 more comments
4
These things were useful when you had to look everything up in tables. But nowadays, with hand-held scientific calculators, we do not need them.
– Gerald Edgar
16 hours ago
2
I don't teach these functions because I don't know what they are. I've heard of only half of them, but even for that half I'd need to look up their definitions. Students can look them up as well as I can.
– Andreas Blass
14 hours ago
2
On the one hand, you could get the answer from Wikipedia articles that you linked. On another hand, I learned something new, so thanks. Not sure why you included chord, which is not a trigonometric function, and is taught at school. As for "popular" functions, sine is useful when studying waves, cosine is useful to find a projection of a force, and tangent is the slope of tangent line, that is, a derivative. I guess finding a trajectory of a ballistic missile is more important nowadays than finding position of a brigantine.
– Rusty Core
13 hours ago
1
@PeterTaylor Thanks, fixed it
– Chris Cunningham
12 hours ago
2
Even with the calculators, I bet almost all students don't even know what a versine is when they see it. --- I don't understand the reasoning behind of this statement. For example, even with calculators, I bet almost all students don't know what a vulgar fraction is when they see it. In fact, even with calculators, I bet almost all students don't know what a syntopogenic space is when they see it. My point is that I don't understand why one would expect students who have a calculator to be more likely to know what a versine is.
– Dave L Renfro
10 hours ago
4
4
These things were useful when you had to look everything up in tables. But nowadays, with hand-held scientific calculators, we do not need them.
– Gerald Edgar
16 hours ago
These things were useful when you had to look everything up in tables. But nowadays, with hand-held scientific calculators, we do not need them.
– Gerald Edgar
16 hours ago
2
2
I don't teach these functions because I don't know what they are. I've heard of only half of them, but even for that half I'd need to look up their definitions. Students can look them up as well as I can.
– Andreas Blass
14 hours ago
I don't teach these functions because I don't know what they are. I've heard of only half of them, but even for that half I'd need to look up their definitions. Students can look them up as well as I can.
– Andreas Blass
14 hours ago
2
2
On the one hand, you could get the answer from Wikipedia articles that you linked. On another hand, I learned something new, so thanks. Not sure why you included chord, which is not a trigonometric function, and is taught at school. As for "popular" functions, sine is useful when studying waves, cosine is useful to find a projection of a force, and tangent is the slope of tangent line, that is, a derivative. I guess finding a trajectory of a ballistic missile is more important nowadays than finding position of a brigantine.
– Rusty Core
13 hours ago
On the one hand, you could get the answer from Wikipedia articles that you linked. On another hand, I learned something new, so thanks. Not sure why you included chord, which is not a trigonometric function, and is taught at school. As for "popular" functions, sine is useful when studying waves, cosine is useful to find a projection of a force, and tangent is the slope of tangent line, that is, a derivative. I guess finding a trajectory of a ballistic missile is more important nowadays than finding position of a brigantine.
– Rusty Core
13 hours ago
1
1
@PeterTaylor Thanks, fixed it
– Chris Cunningham
12 hours ago
@PeterTaylor Thanks, fixed it
– Chris Cunningham
12 hours ago
2
2
Even with the calculators, I bet almost all students don't even know what a versine is when they see it. --- I don't understand the reasoning behind of this statement. For example, even with calculators, I bet almost all students don't know what a vulgar fraction is when they see it. In fact, even with calculators, I bet almost all students don't know what a syntopogenic space is when they see it. My point is that I don't understand why one would expect students who have a calculator to be more likely to know what a versine is.
– Dave L Renfro
10 hours ago
Even with the calculators, I bet almost all students don't even know what a versine is when they see it. --- I don't understand the reasoning behind of this statement. For example, even with calculators, I bet almost all students don't know what a vulgar fraction is when they see it. In fact, even with calculators, I bet almost all students don't know what a syntopogenic space is when they see it. My point is that I don't understand why one would expect students who have a calculator to be more likely to know what a versine is.
– Dave L Renfro
10 hours ago
|
show 7 more comments
3 Answers
3
active
oldest
votes
up vote
10
down vote
More of a comment than an answer but: They are all composites of more basic functions. In fact, all of the trig functions could can expressed in terms of sine, linear changes in coordinates, and rational functions. For instance:
$$
tan(theta) = frac{sin(theta)}{sin( frac{pi}{2}-theta)}
$$
We certainly don't want children to have to memorize 20 different trig functions. That seems a bit silly. Do we even really need to teach all six ``standard'' trig function? Personally I tend to avoid $csc$ and $cot$ in my work...
answered 16 hours ago
Steven Gubkin
8,03812248
5
@Zuriel Indeed, that is the point. There is no mathematical need to teach them. The reason to teach them is because other people know them, and you don't want your students to be confused when they go to their physics classroom and their physics prof uses $cos$. However, the physics prof is probably not going to use the chord function so we can safely ignore it. Perhaps in a hundred years we will have abandoned $csc$. Good riddance I say. $cos$ and $tan$ have a special place in my heart however.
– Steven Gubkin
16 hours ago
4
There isn't a need for cosine in these other fields. I am just saying that the reason we use sine, cosine and tangent, but do not use versine, is the same reason that we use use glasses and don't use monocles: simply that monocles have gone out of fashion, and glasses have not. It is entirely for social reasons that we use some functions and not others. Your education must prepare you to have easy conversation with other people, so we must perpetuate some arbitrary choices to provide ease of communication. This is only one such choice.
– Steven Gubkin
16 hours ago
1
Other choices include the order of function composition, why we do not have a particular name for the antiderivative of sin(1+x^2), the order of operations, that $sqrt(x)$ denotes the positive number whose square is $x$, etc.
– Steven Gubkin
16 hours ago
5
Note that teaching students haversine, versine, etc will actually make it HARDER for them to communicate with others, because most other people have not learned these things. So they would have to find their common ground, and then work out the translations.
– Steven Gubkin
16 hours ago
3
In my heart, cosh and tanh are equally welcome.
– James S. Cook
13 hours ago
|
show 5 more comments
up vote
1
down vote
They are not rarely needed for applications problems in physics or engineering. Really sine, cosine and tangent are mostly what you need. Not even the co-functions.
I'm talking with respect to how formulas and problems are normally written in those courses. Ask yourself, did you encounter those functions in any of your science course and see a need for math to cover them as a service?
I think the versine and such are useful in navigation. But even for celestial nav as of post ww2, it was mostly done with tables and worksheets that don't require you to use these functions (or really know any of the math in what you do). I believe there was a time when there was more need for them before celestial nav became so work sheet oriented. And now celestial nav itself is a dying art because GPS is so common. Ask the average QM to use a sextant and see how he does...
answered 9 hours ago
guest
212
New contributor
guest is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
" Not even the co-functions"... How about cosine then?
– Zuriel
9 hours ago
keep cosine, but ditch secant. I meant the reciprocal functions not needed much. sec, csc, and cot. Sure make the monsters learn it in trig class. Good for them to learn t transform things. But outside of the big 3, they really won't see much in rest of their courses.
– guest
9 hours ago
add a comment |
up vote
1
down vote
Ask yourself if you would miss anything useful if you didn't know the functions you mentioned. I doubt it! I'm teaching high school math happily without having heard of them up to this point.
To the contrary, there are several downsides to teaching them:
Quoting Steven Gubkin's comment: "Note that teaching students haversine, versine, etc will actually make it harder for them to communicate with others, because most other people have not learned these things."- Cognitive overload. Obligatory xkcd.
- Personal opinion: Math should be more about (creative) problem solving than about applying memorized formulas. By not teaching above functions, students can solve more problems by creative usage of $sin$, $cos$, $tan$ and Pythagorean Theorem.
- Calculators. If I express a solution using one of the fancy functions, I'm stuck with a calculator and can't come up with an approximate solution.
answered 9 hours ago
Jasper
524311
I'm surprised no one posted this obligatory link: theonion.com/… "Nation’s Math Teachers Introduce 27 New Trig Functions"
– robphy
5 hours ago
add a comment |
3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
10
down vote
More of a comment than an answer but: They are all composites of more basic functions. In fact, all of the trig functions could can expressed in terms of sine, linear changes in coordinates, and rational functions. For instance:
$$
tan(theta) = frac{sin(theta)}{sin( frac{pi}{2}-theta)}
$$
We certainly don't want children to have to memorize 20 different trig functions. That seems a bit silly. Do we even really need to teach all six ``standard'' trig function? Personally I tend to avoid $csc$ and $cot$ in my work...
answered 16 hours ago
Steven Gubkin
8,03812248
5
@Zuriel Indeed, that is the point. There is no mathematical need to teach them. The reason to teach them is because other people know them, and you don't want your students to be confused when they go to their physics classroom and their physics prof uses $cos$. However, the physics prof is probably not going to use the chord function so we can safely ignore it. Perhaps in a hundred years we will have abandoned $csc$. Good riddance I say. $cos$ and $tan$ have a special place in my heart however.
– Steven Gubkin
16 hours ago
4
There isn't a need for cosine in these other fields. I am just saying that the reason we use sine, cosine and tangent, but do not use versine, is the same reason that we use use glasses and don't use monocles: simply that monocles have gone out of fashion, and glasses have not. It is entirely for social reasons that we use some functions and not others. Your education must prepare you to have easy conversation with other people, so we must perpetuate some arbitrary choices to provide ease of communication. This is only one such choice.
– Steven Gubkin
16 hours ago
1
Other choices include the order of function composition, why we do not have a particular name for the antiderivative of sin(1+x^2), the order of operations, that $sqrt(x)$ denotes the positive number whose square is $x$, etc.
– Steven Gubkin
16 hours ago
5
Note that teaching students haversine, versine, etc will actually make it HARDER for them to communicate with others, because most other people have not learned these things. So they would have to find their common ground, and then work out the translations.
– Steven Gubkin
16 hours ago
3
In my heart, cosh and tanh are equally welcome.
– James S. Cook
13 hours ago
|
show 5 more comments
up vote
10
down vote
More of a comment than an answer but: They are all composites of more basic functions. In fact, all of the trig functions could can expressed in terms of sine, linear changes in coordinates, and rational functions. For instance:
$$
tan(theta) = frac{sin(theta)}{sin( frac{pi}{2}-theta)}
$$
We certainly don't want children to have to memorize 20 different trig functions. That seems a bit silly. Do we even really need to teach all six ``standard'' trig function? Personally I tend to avoid $csc$ and $cot$ in my work...
answered 16 hours ago
Steven Gubkin
8,03812248
5
@Zuriel Indeed, that is the point. There is no mathematical need to teach them. The reason to teach them is because other people know them, and you don't want your students to be confused when they go to their physics classroom and their physics prof uses $cos$. However, the physics prof is probably not going to use the chord function so we can safely ignore it. Perhaps in a hundred years we will have abandoned $csc$. Good riddance I say. $cos$ and $tan$ have a special place in my heart however.
– Steven Gubkin
16 hours ago
4
There isn't a need for cosine in these other fields. I am just saying that the reason we use sine, cosine and tangent, but do not use versine, is the same reason that we use use glasses and don't use monocles: simply that monocles have gone out of fashion, and glasses have not. It is entirely for social reasons that we use some functions and not others. Your education must prepare you to have easy conversation with other people, so we must perpetuate some arbitrary choices to provide ease of communication. This is only one such choice.
– Steven Gubkin
16 hours ago
1
Other choices include the order of function composition, why we do not have a particular name for the antiderivative of sin(1+x^2), the order of operations, that $sqrt(x)$ denotes the positive number whose square is $x$, etc.
– Steven Gubkin
16 hours ago
5
Note that teaching students haversine, versine, etc will actually make it HARDER for them to communicate with others, because most other people have not learned these things. So they would have to find their common ground, and then work out the translations.
– Steven Gubkin
16 hours ago
3
In my heart, cosh and tanh are equally welcome.
– James S. Cook
13 hours ago
|
show 5 more comments
up vote
10
down vote
up vote
10
down vote
More of a comment than an answer but: They are all composites of more basic functions. In fact, all of the trig functions could can expressed in terms of sine, linear changes in coordinates, and rational functions. For instance:
$$
tan(theta) = frac{sin(theta)}{sin( frac{pi}{2}-theta)}
$$
We certainly don't want children to have to memorize 20 different trig functions. That seems a bit silly. Do we even really need to teach all six ``standard'' trig function? Personally I tend to avoid $csc$ and $cot$ in my work...
answered 16 hours ago
Steven Gubkin
8,03812248
More of a comment than an answer but: They are all composites of more basic functions. In fact, all of the trig functions could can expressed in terms of sine, linear changes in coordinates, and rational functions. For instance:
$$
tan(theta) = frac{sin(theta)}{sin( frac{pi}{2}-theta)}
$$
We certainly don't want children to have to memorize 20 different trig functions. That seems a bit silly. Do we even really need to teach all six ``standard'' trig function? Personally I tend to avoid $csc$ and $cot$ in my work...
answered 16 hours ago
Steven Gubkin
8,03812248
answered 16 hours ago
Steven Gubkin
8,03812248
answered 16 hours ago
Steven Gubkin
8,03812248
answered 16 hours ago
Steven Gubkin
8,03812248
8,03812248
5
@Zuriel Indeed, that is the point. There is no mathematical need to teach them. The reason to teach them is because other people know them, and you don't want your students to be confused when they go to their physics classroom and their physics prof uses $cos$. However, the physics prof is probably not going to use the chord function so we can safely ignore it. Perhaps in a hundred years we will have abandoned $csc$. Good riddance I say. $cos$ and $tan$ have a special place in my heart however.
– Steven Gubkin
16 hours ago
4
There isn't a need for cosine in these other fields. I am just saying that the reason we use sine, cosine and tangent, but do not use versine, is the same reason that we use use glasses and don't use monocles: simply that monocles have gone out of fashion, and glasses have not. It is entirely for social reasons that we use some functions and not others. Your education must prepare you to have easy conversation with other people, so we must perpetuate some arbitrary choices to provide ease of communication. This is only one such choice.
– Steven Gubkin
16 hours ago
1
Other choices include the order of function composition, why we do not have a particular name for the antiderivative of sin(1+x^2), the order of operations, that $sqrt(x)$ denotes the positive number whose square is $x$, etc.
– Steven Gubkin
16 hours ago
5
Note that teaching students haversine, versine, etc will actually make it HARDER for them to communicate with others, because most other people have not learned these things. So they would have to find their common ground, and then work out the translations.
– Steven Gubkin
16 hours ago
3
In my heart, cosh and tanh are equally welcome.
– James S. Cook
13 hours ago
|
show 5 more comments
5
@Zuriel Indeed, that is the point. There is no mathematical need to teach them. The reason to teach them is because other people know them, and you don't want your students to be confused when they go to their physics classroom and their physics prof uses $cos$. However, the physics prof is probably not going to use the chord function so we can safely ignore it. Perhaps in a hundred years we will have abandoned $csc$. Good riddance I say. $cos$ and $tan$ have a special place in my heart however.
– Steven Gubkin
16 hours ago
4
There isn't a need for cosine in these other fields. I am just saying that the reason we use sine, cosine and tangent, but do not use versine, is the same reason that we use use glasses and don't use monocles: simply that monocles have gone out of fashion, and glasses have not. It is entirely for social reasons that we use some functions and not others. Your education must prepare you to have easy conversation with other people, so we must perpetuate some arbitrary choices to provide ease of communication. This is only one such choice.
– Steven Gubkin
16 hours ago
1
Other choices include the order of function composition, why we do not have a particular name for the antiderivative of sin(1+x^2), the order of operations, that $sqrt(x)$ denotes the positive number whose square is $x$, etc.
– Steven Gubkin
16 hours ago
5
Note that teaching students haversine, versine, etc will actually make it HARDER for them to communicate with others, because most other people have not learned these things. So they would have to find their common ground, and then work out the translations.
– Steven Gubkin
16 hours ago
3
In my heart, cosh and tanh are equally welcome.
– James S. Cook
13 hours ago
5
5
@Zuriel Indeed, that is the point. There is no mathematical need to teach them. The reason to teach them is because other people know them, and you don't want your students to be confused when they go to their physics classroom and their physics prof uses $cos$. However, the physics prof is probably not going to use the chord function so we can safely ignore it. Perhaps in a hundred years we will have abandoned $csc$. Good riddance I say. $cos$ and $tan$ have a special place in my heart however.
– Steven Gubkin
16 hours ago
@Zuriel Indeed, that is the point. There is no mathematical need to teach them. The reason to teach them is because other people know them, and you don't want your students to be confused when they go to their physics classroom and their physics prof uses $cos$. However, the physics prof is probably not going to use the chord function so we can safely ignore it. Perhaps in a hundred years we will have abandoned $csc$. Good riddance I say. $cos$ and $tan$ have a special place in my heart however.
– Steven Gubkin
16 hours ago
4
4
There isn't a need for cosine in these other fields. I am just saying that the reason we use sine, cosine and tangent, but do not use versine, is the same reason that we use use glasses and don't use monocles: simply that monocles have gone out of fashion, and glasses have not. It is entirely for social reasons that we use some functions and not others. Your education must prepare you to have easy conversation with other people, so we must perpetuate some arbitrary choices to provide ease of communication. This is only one such choice.
– Steven Gubkin
16 hours ago
There isn't a need for cosine in these other fields. I am just saying that the reason we use sine, cosine and tangent, but do not use versine, is the same reason that we use use glasses and don't use monocles: simply that monocles have gone out of fashion, and glasses have not. It is entirely for social reasons that we use some functions and not others. Your education must prepare you to have easy conversation with other people, so we must perpetuate some arbitrary choices to provide ease of communication. This is only one such choice.
– Steven Gubkin
16 hours ago
1
1
Other choices include the order of function composition, why we do not have a particular name for the antiderivative of sin(1+x^2), the order of operations, that $sqrt(x)$ denotes the positive number whose square is $x$, etc.
– Steven Gubkin
16 hours ago
Other choices include the order of function composition, why we do not have a particular name for the antiderivative of sin(1+x^2), the order of operations, that $sqrt(x)$ denotes the positive number whose square is $x$, etc.
– Steven Gubkin
16 hours ago
5
5
Note that teaching students haversine, versine, etc will actually make it HARDER for them to communicate with others, because most other people have not learned these things. So they would have to find their common ground, and then work out the translations.
– Steven Gubkin
16 hours ago
Note that teaching students haversine, versine, etc will actually make it HARDER for them to communicate with others, because most other people have not learned these things. So they would have to find their common ground, and then work out the translations.
– Steven Gubkin
16 hours ago
3
3
In my heart, cosh and tanh are equally welcome.
– James S. Cook
13 hours ago
In my heart, cosh and tanh are equally welcome.
– James S. Cook
13 hours ago
|
show 5 more comments
up vote
1
down vote
They are not rarely needed for applications problems in physics or engineering. Really sine, cosine and tangent are mostly what you need. Not even the co-functions.
I'm talking with respect to how formulas and problems are normally written in those courses. Ask yourself, did you encounter those functions in any of your science course and see a need for math to cover them as a service?
I think the versine and such are useful in navigation. But even for celestial nav as of post ww2, it was mostly done with tables and worksheets that don't require you to use these functions (or really know any of the math in what you do). I believe there was a time when there was more need for them before celestial nav became so work sheet oriented. And now celestial nav itself is a dying art because GPS is so common. Ask the average QM to use a sextant and see how he does...
answered 9 hours ago
guest
212
New contributor
guest is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
" Not even the co-functions"... How about cosine then?
– Zuriel
9 hours ago
keep cosine, but ditch secant. I meant the reciprocal functions not needed much. sec, csc, and cot. Sure make the monsters learn it in trig class. Good for them to learn t transform things. But outside of the big 3, they really won't see much in rest of their courses.
– guest
9 hours ago
add a comment |
up vote
1
down vote
They are not rarely needed for applications problems in physics or engineering. Really sine, cosine and tangent are mostly what you need. Not even the co-functions.
I'm talking with respect to how formulas and problems are normally written in those courses. Ask yourself, did you encounter those functions in any of your science course and see a need for math to cover them as a service?
I think the versine and such are useful in navigation. But even for celestial nav as of post ww2, it was mostly done with tables and worksheets that don't require you to use these functions (or really know any of the math in what you do). I believe there was a time when there was more need for them before celestial nav became so work sheet oriented. And now celestial nav itself is a dying art because GPS is so common. Ask the average QM to use a sextant and see how he does...
answered 9 hours ago
guest
212
New contributor
guest is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
1
" Not even the co-functions"... How about cosine then?
– Zuriel
9 hours ago
keep cosine, but ditch secant. I meant the reciprocal functions not needed much. sec, csc, and cot. Sure make the monsters learn it in trig class. Good for them to learn t transform things. But outside of the big 3, they really won't see much in rest of their courses.
– guest
9 hours ago
add a comment |
up vote
1
down vote
up vote
1
down vote
They are not rarely needed for applications problems in physics or engineering. Really sine, cosine and tangent are mostly what you need. Not even the co-functions.
I'm talking with respect to how formulas and problems are normally written in those courses. Ask yourself, did you encounter those functions in any of your science course and see a need for math to cover them as a service?
I think the versine and such are useful in navigation. But even for celestial nav as of post ww2, it was mostly done with tables and worksheets that don't require you to use these functions (or really know any of the math in what you do). I believe there was a time when there was more need for them before celestial nav became so work sheet oriented. And now celestial nav itself is a dying art because GPS is so common. Ask the average QM to use a sextant and see how he does...
answered 9 hours ago
guest
212
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guest is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
They are not rarely needed for applications problems in physics or engineering. Really sine, cosine and tangent are mostly what you need. Not even the co-functions.
I'm talking with respect to how formulas and problems are normally written in those courses. Ask yourself, did you encounter those functions in any of your science course and see a need for math to cover them as a service?
I think the versine and such are useful in navigation. But even for celestial nav as of post ww2, it was mostly done with tables and worksheets that don't require you to use these functions (or really know any of the math in what you do). I believe there was a time when there was more need for them before celestial nav became so work sheet oriented. And now celestial nav itself is a dying art because GPS is so common. Ask the average QM to use a sextant and see how he does...
answered 9 hours ago
guest
212
New contributor
guest is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 9 hours ago
guest
212
New contributor
guest is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
answered 9 hours ago
guest
212
answered 9 hours ago
guest
212
212
New contributor
guest is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
New contributor
guest is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.
guest is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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1
" Not even the co-functions"... How about cosine then?
– Zuriel
9 hours ago
keep cosine, but ditch secant. I meant the reciprocal functions not needed much. sec, csc, and cot. Sure make the monsters learn it in trig class. Good for them to learn t transform things. But outside of the big 3, they really won't see much in rest of their courses.
– guest
9 hours ago
add a comment |
1
" Not even the co-functions"... How about cosine then?
– Zuriel
9 hours ago
keep cosine, but ditch secant. I meant the reciprocal functions not needed much. sec, csc, and cot. Sure make the monsters learn it in trig class. Good for them to learn t transform things. But outside of the big 3, they really won't see much in rest of their courses.
– guest
9 hours ago
1
1
" Not even the co-functions"... How about cosine then?
– Zuriel
9 hours ago
" Not even the co-functions"... How about cosine then?
– Zuriel
9 hours ago
keep cosine, but ditch secant. I meant the reciprocal functions not needed much. sec, csc, and cot. Sure make the monsters learn it in trig class. Good for them to learn t transform things. But outside of the big 3, they really won't see much in rest of their courses.
– guest
9 hours ago
keep cosine, but ditch secant. I meant the reciprocal functions not needed much. sec, csc, and cot. Sure make the monsters learn it in trig class. Good for them to learn t transform things. But outside of the big 3, they really won't see much in rest of their courses.
– guest
9 hours ago
add a comment |
up vote
1
down vote
Ask yourself if you would miss anything useful if you didn't know the functions you mentioned. I doubt it! I'm teaching high school math happily without having heard of them up to this point.
To the contrary, there are several downsides to teaching them:
Quoting Steven Gubkin's comment: "Note that teaching students haversine, versine, etc will actually make it harder for them to communicate with others, because most other people have not learned these things."- Cognitive overload. Obligatory xkcd.
- Personal opinion: Math should be more about (creative) problem solving than about applying memorized formulas. By not teaching above functions, students can solve more problems by creative usage of $sin$, $cos$, $tan$ and Pythagorean Theorem.
- Calculators. If I express a solution using one of the fancy functions, I'm stuck with a calculator and can't come up with an approximate solution.
answered 9 hours ago
Jasper
524311
I'm surprised no one posted this obligatory link: theonion.com/… "Nation’s Math Teachers Introduce 27 New Trig Functions"
– robphy
5 hours ago
add a comment |
up vote
1
down vote
Ask yourself if you would miss anything useful if you didn't know the functions you mentioned. I doubt it! I'm teaching high school math happily without having heard of them up to this point.
To the contrary, there are several downsides to teaching them:
Quoting Steven Gubkin's comment: "Note that teaching students haversine, versine, etc will actually make it harder for them to communicate with others, because most other people have not learned these things."- Cognitive overload. Obligatory xkcd.
- Personal opinion: Math should be more about (creative) problem solving than about applying memorized formulas. By not teaching above functions, students can solve more problems by creative usage of $sin$, $cos$, $tan$ and Pythagorean Theorem.
- Calculators. If I express a solution using one of the fancy functions, I'm stuck with a calculator and can't come up with an approximate solution.
answered 9 hours ago
Jasper
524311
I'm surprised no one posted this obligatory link: theonion.com/… "Nation’s Math Teachers Introduce 27 New Trig Functions"
– robphy
5 hours ago
add a comment |
up vote
1
down vote
up vote
1
down vote
Ask yourself if you would miss anything useful if you didn't know the functions you mentioned. I doubt it! I'm teaching high school math happily without having heard of them up to this point.
To the contrary, there are several downsides to teaching them:
Quoting Steven Gubkin's comment: "Note that teaching students haversine, versine, etc will actually make it harder for them to communicate with others, because most other people have not learned these things."- Cognitive overload. Obligatory xkcd.
- Personal opinion: Math should be more about (creative) problem solving than about applying memorized formulas. By not teaching above functions, students can solve more problems by creative usage of $sin$, $cos$, $tan$ and Pythagorean Theorem.
- Calculators. If I express a solution using one of the fancy functions, I'm stuck with a calculator and can't come up with an approximate solution.
answered 9 hours ago
Jasper
524311
Ask yourself if you would miss anything useful if you didn't know the functions you mentioned. I doubt it! I'm teaching high school math happily without having heard of them up to this point.
To the contrary, there are several downsides to teaching them:
Quoting Steven Gubkin's comment: "Note that teaching students haversine, versine, etc will actually make it harder for them to communicate with others, because most other people have not learned these things."- Cognitive overload. Obligatory xkcd.
- Personal opinion: Math should be more about (creative) problem solving than about applying memorized formulas. By not teaching above functions, students can solve more problems by creative usage of $sin$, $cos$, $tan$ and Pythagorean Theorem.
- Calculators. If I express a solution using one of the fancy functions, I'm stuck with a calculator and can't come up with an approximate solution.
answered 9 hours ago
Jasper
524311
edited 17 mins ago
answered 9 hours ago
Jasper
524311
answered 9 hours ago
Jasper
524311
answered 9 hours ago
Jasper
524311
524311
I'm surprised no one posted this obligatory link: theonion.com/… "Nation’s Math Teachers Introduce 27 New Trig Functions"
– robphy
5 hours ago
add a comment |
I'm surprised no one posted this obligatory link: theonion.com/… "Nation’s Math Teachers Introduce 27 New Trig Functions"
– robphy
5 hours ago
I'm surprised no one posted this obligatory link: theonion.com/… "Nation’s Math Teachers Introduce 27 New Trig Functions"
– robphy
5 hours ago
I'm surprised no one posted this obligatory link: theonion.com/… "Nation’s Math Teachers Introduce 27 New Trig Functions"
– robphy
5 hours ago
add a comment |
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4
These things were useful when you had to look everything up in tables. But nowadays, with hand-held scientific calculators, we do not need them.
– Gerald Edgar
16 hours ago
2
I don't teach these functions because I don't know what they are. I've heard of only half of them, but even for that half I'd need to look up their definitions. Students can look them up as well as I can.
– Andreas Blass
14 hours ago
2
On the one hand, you could get the answer from Wikipedia articles that you linked. On another hand, I learned something new, so thanks. Not sure why you included chord, which is not a trigonometric function, and is taught at school. As for "popular" functions, sine is useful when studying waves, cosine is useful to find a projection of a force, and tangent is the slope of tangent line, that is, a derivative. I guess finding a trajectory of a ballistic missile is more important nowadays than finding position of a brigantine.
– Rusty Core
13 hours ago
1
@PeterTaylor Thanks, fixed it
– Chris Cunningham
12 hours ago
2
Even with the calculators, I bet almost all students don't even know what a versine is when they see it. --- I don't understand the reasoning behind of this statement. For example, even with calculators, I bet almost all students don't know what a vulgar fraction is when they see it. In fact, even with calculators, I bet almost all students don't know what a syntopogenic space is when they see it. My point is that I don't understand why one would expect students who have a calculator to be more likely to know what a versine is.
– Dave L Renfro
10 hours ago