Learning $arcsin, arccos, arctan$ - how to?
$begingroup$
Sorry for asking such question.
I have a very basic understanding of $arcsin, arccos, arctan$ functions. I do know how their graph looks like and not much more beyond that.
Calculate:
Which specific keywords should I google to learn how to solve the following tasks? I think those aren't equations (googling 'cyclometric equations' was a dead end). Perhaps you would like to share with some link to a beginner-friendly learning source?
Thank you.
analysis trigonometry inverse-function
$endgroup$
|
show 2 more comments
$begingroup$
Sorry for asking such question.
I have a very basic understanding of $arcsin, arccos, arctan$ functions. I do know how their graph looks like and not much more beyond that.
Calculate:
Which specific keywords should I google to learn how to solve the following tasks? I think those aren't equations (googling 'cyclometric equations' was a dead end). Perhaps you would like to share with some link to a beginner-friendly learning source?
Thank you.
analysis trigonometry inverse-function
$endgroup$
1
$begingroup$
inverse trigonometric functions is what I would call them
$endgroup$
– Henry Lee
Dec 5 '18 at 1:06
1
$begingroup$
also a lot of them just require the compound angle formula or some rearrangment to make them a lot easier
$endgroup$
– Henry Lee
Dec 5 '18 at 1:07
1
$begingroup$
"cyclometric" is the old name for the inverse trig functions. Any basic book should have sections on how to evaluate these.
$endgroup$
– SZN
Dec 5 '18 at 1:11
1
$begingroup$
these are more simple but a start: tutorial.math.lamar.edu/Extras/AlgebraTrigReview/…
$endgroup$
– Henry Lee
Dec 5 '18 at 1:11
1
$begingroup$
if you ask specifically about 1 of those questions that you struggle with people will also help
$endgroup$
– Henry Lee
Dec 5 '18 at 1:12
|
show 2 more comments
$begingroup$
Sorry for asking such question.
I have a very basic understanding of $arcsin, arccos, arctan$ functions. I do know how their graph looks like and not much more beyond that.
Calculate:
Which specific keywords should I google to learn how to solve the following tasks? I think those aren't equations (googling 'cyclometric equations' was a dead end). Perhaps you would like to share with some link to a beginner-friendly learning source?
Thank you.
analysis trigonometry inverse-function
$endgroup$
Sorry for asking such question.
I have a very basic understanding of $arcsin, arccos, arctan$ functions. I do know how their graph looks like and not much more beyond that.
Calculate:
Which specific keywords should I google to learn how to solve the following tasks? I think those aren't equations (googling 'cyclometric equations' was a dead end). Perhaps you would like to share with some link to a beginner-friendly learning source?
Thank you.
analysis trigonometry inverse-function
analysis trigonometry inverse-function
asked Dec 5 '18 at 1:05
wenoweno
30511
30511
1
$begingroup$
inverse trigonometric functions is what I would call them
$endgroup$
– Henry Lee
Dec 5 '18 at 1:06
1
$begingroup$
also a lot of them just require the compound angle formula or some rearrangment to make them a lot easier
$endgroup$
– Henry Lee
Dec 5 '18 at 1:07
1
$begingroup$
"cyclometric" is the old name for the inverse trig functions. Any basic book should have sections on how to evaluate these.
$endgroup$
– SZN
Dec 5 '18 at 1:11
1
$begingroup$
these are more simple but a start: tutorial.math.lamar.edu/Extras/AlgebraTrigReview/…
$endgroup$
– Henry Lee
Dec 5 '18 at 1:11
1
$begingroup$
if you ask specifically about 1 of those questions that you struggle with people will also help
$endgroup$
– Henry Lee
Dec 5 '18 at 1:12
|
show 2 more comments
1
$begingroup$
inverse trigonometric functions is what I would call them
$endgroup$
– Henry Lee
Dec 5 '18 at 1:06
1
$begingroup$
also a lot of them just require the compound angle formula or some rearrangment to make them a lot easier
$endgroup$
– Henry Lee
Dec 5 '18 at 1:07
1
$begingroup$
"cyclometric" is the old name for the inverse trig functions. Any basic book should have sections on how to evaluate these.
$endgroup$
– SZN
Dec 5 '18 at 1:11
1
$begingroup$
these are more simple but a start: tutorial.math.lamar.edu/Extras/AlgebraTrigReview/…
$endgroup$
– Henry Lee
Dec 5 '18 at 1:11
1
$begingroup$
if you ask specifically about 1 of those questions that you struggle with people will also help
$endgroup$
– Henry Lee
Dec 5 '18 at 1:12
1
1
$begingroup$
inverse trigonometric functions is what I would call them
$endgroup$
– Henry Lee
Dec 5 '18 at 1:06
$begingroup$
inverse trigonometric functions is what I would call them
$endgroup$
– Henry Lee
Dec 5 '18 at 1:06
1
1
$begingroup$
also a lot of them just require the compound angle formula or some rearrangment to make them a lot easier
$endgroup$
– Henry Lee
Dec 5 '18 at 1:07
$begingroup$
also a lot of them just require the compound angle formula or some rearrangment to make them a lot easier
$endgroup$
– Henry Lee
Dec 5 '18 at 1:07
1
1
$begingroup$
"cyclometric" is the old name for the inverse trig functions. Any basic book should have sections on how to evaluate these.
$endgroup$
– SZN
Dec 5 '18 at 1:11
$begingroup$
"cyclometric" is the old name for the inverse trig functions. Any basic book should have sections on how to evaluate these.
$endgroup$
– SZN
Dec 5 '18 at 1:11
1
1
$begingroup$
these are more simple but a start: tutorial.math.lamar.edu/Extras/AlgebraTrigReview/…
$endgroup$
– Henry Lee
Dec 5 '18 at 1:11
$begingroup$
these are more simple but a start: tutorial.math.lamar.edu/Extras/AlgebraTrigReview/…
$endgroup$
– Henry Lee
Dec 5 '18 at 1:11
1
1
$begingroup$
if you ask specifically about 1 of those questions that you struggle with people will also help
$endgroup$
– Henry Lee
Dec 5 '18 at 1:12
$begingroup$
if you ask specifically about 1 of those questions that you struggle with people will also help
$endgroup$
– Henry Lee
Dec 5 '18 at 1:12
|
show 2 more comments
3 Answers
3
active
oldest
votes
$begingroup$
I would say there are three things you are expected to do on this list. One is to know the trig functions of special angles, so for 4 you should know that $tan frac pi 4=1,$ so $arctan 1=frac pi 4$ Watch out for the ranges specified for the inverse trig functions. Second is that $sin(arcsin (x))=x$. When you have $arcsin (sin(x))$ you may be shifted by factors of $pi$. Finally when you have $sin(arccos(frac 13))$ draw a right triangle with $cos$ of one angle $frac 13$, so it is a $1-sqrt 8-3$ triangle and find the sine of the angle, here $frac 13sqrt 8$.
$endgroup$
$begingroup$
Hey, thanks. I understood everything except for: "When you have arcsin(sin(x)) you may be shifted by factors of π". Would you give a little bit more insight on this?
$endgroup$
– weno
Dec 5 '18 at 1:19
$begingroup$
The range of $arcsin$ is defined as $[-frac pi 2,frac pi 2]$, so if we are asked for $arcsin(sin(frac {9pi}4))$ the answer is $frac pi 4,$ not $frac {9 pi}4$
$endgroup$
– Ross Millikan
Dec 5 '18 at 1:22
$begingroup$
Those indeed are the tricky questions which I was referring to!
$endgroup$
– gimusi
Dec 5 '18 at 1:23
$begingroup$
I don't know which post should I accept, since you both helped me a lot. I'll do a random.org roll.
$endgroup$
– weno
Dec 5 '18 at 1:29
add a comment |
$begingroup$
Some good reference as summary from Wikipedia are
- List of trigonometric identities
and also
- Inverse trigonometric functions
Some exercises given requires only to calculate the value for the functions at some point, other else are more tricky and you need to acquire a deeply understanding of the matter.
Refer also to the related
Reference Request: Book for Trigonometry and Geometry
Good book on advanced trig
$endgroup$
$begingroup$
That should help, thanks.
$endgroup$
– weno
Dec 5 '18 at 1:14
$begingroup$
Do not hesitate to ask for any exercise in particular! Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:15
$begingroup$
I would, but unless I made any significant progress myself, I don't think anyone will solve that for me. :)
$endgroup$
– weno
Dec 5 '18 at 1:17
$begingroup$
That’s nice but in case of doubt I would happy to check that with you. Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:19
add a comment |
$begingroup$
This lecture has been particularly helpful on understanding the subject:
https://academics.utep.edu/Portals/1788/CALCULUS%20MATERIAL/4_7%20INVERSE%20TRIG%20FNS.pdf
$endgroup$
add a comment |
Your Answer
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3 Answers
3
active
oldest
votes
3 Answers
3
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
I would say there are three things you are expected to do on this list. One is to know the trig functions of special angles, so for 4 you should know that $tan frac pi 4=1,$ so $arctan 1=frac pi 4$ Watch out for the ranges specified for the inverse trig functions. Second is that $sin(arcsin (x))=x$. When you have $arcsin (sin(x))$ you may be shifted by factors of $pi$. Finally when you have $sin(arccos(frac 13))$ draw a right triangle with $cos$ of one angle $frac 13$, so it is a $1-sqrt 8-3$ triangle and find the sine of the angle, here $frac 13sqrt 8$.
$endgroup$
$begingroup$
Hey, thanks. I understood everything except for: "When you have arcsin(sin(x)) you may be shifted by factors of π". Would you give a little bit more insight on this?
$endgroup$
– weno
Dec 5 '18 at 1:19
$begingroup$
The range of $arcsin$ is defined as $[-frac pi 2,frac pi 2]$, so if we are asked for $arcsin(sin(frac {9pi}4))$ the answer is $frac pi 4,$ not $frac {9 pi}4$
$endgroup$
– Ross Millikan
Dec 5 '18 at 1:22
$begingroup$
Those indeed are the tricky questions which I was referring to!
$endgroup$
– gimusi
Dec 5 '18 at 1:23
$begingroup$
I don't know which post should I accept, since you both helped me a lot. I'll do a random.org roll.
$endgroup$
– weno
Dec 5 '18 at 1:29
add a comment |
$begingroup$
I would say there are three things you are expected to do on this list. One is to know the trig functions of special angles, so for 4 you should know that $tan frac pi 4=1,$ so $arctan 1=frac pi 4$ Watch out for the ranges specified for the inverse trig functions. Second is that $sin(arcsin (x))=x$. When you have $arcsin (sin(x))$ you may be shifted by factors of $pi$. Finally when you have $sin(arccos(frac 13))$ draw a right triangle with $cos$ of one angle $frac 13$, so it is a $1-sqrt 8-3$ triangle and find the sine of the angle, here $frac 13sqrt 8$.
$endgroup$
$begingroup$
Hey, thanks. I understood everything except for: "When you have arcsin(sin(x)) you may be shifted by factors of π". Would you give a little bit more insight on this?
$endgroup$
– weno
Dec 5 '18 at 1:19
$begingroup$
The range of $arcsin$ is defined as $[-frac pi 2,frac pi 2]$, so if we are asked for $arcsin(sin(frac {9pi}4))$ the answer is $frac pi 4,$ not $frac {9 pi}4$
$endgroup$
– Ross Millikan
Dec 5 '18 at 1:22
$begingroup$
Those indeed are the tricky questions which I was referring to!
$endgroup$
– gimusi
Dec 5 '18 at 1:23
$begingroup$
I don't know which post should I accept, since you both helped me a lot. I'll do a random.org roll.
$endgroup$
– weno
Dec 5 '18 at 1:29
add a comment |
$begingroup$
I would say there are three things you are expected to do on this list. One is to know the trig functions of special angles, so for 4 you should know that $tan frac pi 4=1,$ so $arctan 1=frac pi 4$ Watch out for the ranges specified for the inverse trig functions. Second is that $sin(arcsin (x))=x$. When you have $arcsin (sin(x))$ you may be shifted by factors of $pi$. Finally when you have $sin(arccos(frac 13))$ draw a right triangle with $cos$ of one angle $frac 13$, so it is a $1-sqrt 8-3$ triangle and find the sine of the angle, here $frac 13sqrt 8$.
$endgroup$
I would say there are three things you are expected to do on this list. One is to know the trig functions of special angles, so for 4 you should know that $tan frac pi 4=1,$ so $arctan 1=frac pi 4$ Watch out for the ranges specified for the inverse trig functions. Second is that $sin(arcsin (x))=x$. When you have $arcsin (sin(x))$ you may be shifted by factors of $pi$. Finally when you have $sin(arccos(frac 13))$ draw a right triangle with $cos$ of one angle $frac 13$, so it is a $1-sqrt 8-3$ triangle and find the sine of the angle, here $frac 13sqrt 8$.
edited Dec 5 '18 at 1:56
answered Dec 5 '18 at 1:17
Ross MillikanRoss Millikan
295k23198371
295k23198371
$begingroup$
Hey, thanks. I understood everything except for: "When you have arcsin(sin(x)) you may be shifted by factors of π". Would you give a little bit more insight on this?
$endgroup$
– weno
Dec 5 '18 at 1:19
$begingroup$
The range of $arcsin$ is defined as $[-frac pi 2,frac pi 2]$, so if we are asked for $arcsin(sin(frac {9pi}4))$ the answer is $frac pi 4,$ not $frac {9 pi}4$
$endgroup$
– Ross Millikan
Dec 5 '18 at 1:22
$begingroup$
Those indeed are the tricky questions which I was referring to!
$endgroup$
– gimusi
Dec 5 '18 at 1:23
$begingroup$
I don't know which post should I accept, since you both helped me a lot. I'll do a random.org roll.
$endgroup$
– weno
Dec 5 '18 at 1:29
add a comment |
$begingroup$
Hey, thanks. I understood everything except for: "When you have arcsin(sin(x)) you may be shifted by factors of π". Would you give a little bit more insight on this?
$endgroup$
– weno
Dec 5 '18 at 1:19
$begingroup$
The range of $arcsin$ is defined as $[-frac pi 2,frac pi 2]$, so if we are asked for $arcsin(sin(frac {9pi}4))$ the answer is $frac pi 4,$ not $frac {9 pi}4$
$endgroup$
– Ross Millikan
Dec 5 '18 at 1:22
$begingroup$
Those indeed are the tricky questions which I was referring to!
$endgroup$
– gimusi
Dec 5 '18 at 1:23
$begingroup$
I don't know which post should I accept, since you both helped me a lot. I'll do a random.org roll.
$endgroup$
– weno
Dec 5 '18 at 1:29
$begingroup$
Hey, thanks. I understood everything except for: "When you have arcsin(sin(x)) you may be shifted by factors of π". Would you give a little bit more insight on this?
$endgroup$
– weno
Dec 5 '18 at 1:19
$begingroup$
Hey, thanks. I understood everything except for: "When you have arcsin(sin(x)) you may be shifted by factors of π". Would you give a little bit more insight on this?
$endgroup$
– weno
Dec 5 '18 at 1:19
$begingroup$
The range of $arcsin$ is defined as $[-frac pi 2,frac pi 2]$, so if we are asked for $arcsin(sin(frac {9pi}4))$ the answer is $frac pi 4,$ not $frac {9 pi}4$
$endgroup$
– Ross Millikan
Dec 5 '18 at 1:22
$begingroup$
The range of $arcsin$ is defined as $[-frac pi 2,frac pi 2]$, so if we are asked for $arcsin(sin(frac {9pi}4))$ the answer is $frac pi 4,$ not $frac {9 pi}4$
$endgroup$
– Ross Millikan
Dec 5 '18 at 1:22
$begingroup$
Those indeed are the tricky questions which I was referring to!
$endgroup$
– gimusi
Dec 5 '18 at 1:23
$begingroup$
Those indeed are the tricky questions which I was referring to!
$endgroup$
– gimusi
Dec 5 '18 at 1:23
$begingroup$
I don't know which post should I accept, since you both helped me a lot. I'll do a random.org roll.
$endgroup$
– weno
Dec 5 '18 at 1:29
$begingroup$
I don't know which post should I accept, since you both helped me a lot. I'll do a random.org roll.
$endgroup$
– weno
Dec 5 '18 at 1:29
add a comment |
$begingroup$
Some good reference as summary from Wikipedia are
- List of trigonometric identities
and also
- Inverse trigonometric functions
Some exercises given requires only to calculate the value for the functions at some point, other else are more tricky and you need to acquire a deeply understanding of the matter.
Refer also to the related
Reference Request: Book for Trigonometry and Geometry
Good book on advanced trig
$endgroup$
$begingroup$
That should help, thanks.
$endgroup$
– weno
Dec 5 '18 at 1:14
$begingroup$
Do not hesitate to ask for any exercise in particular! Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:15
$begingroup$
I would, but unless I made any significant progress myself, I don't think anyone will solve that for me. :)
$endgroup$
– weno
Dec 5 '18 at 1:17
$begingroup$
That’s nice but in case of doubt I would happy to check that with you. Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:19
add a comment |
$begingroup$
Some good reference as summary from Wikipedia are
- List of trigonometric identities
and also
- Inverse trigonometric functions
Some exercises given requires only to calculate the value for the functions at some point, other else are more tricky and you need to acquire a deeply understanding of the matter.
Refer also to the related
Reference Request: Book for Trigonometry and Geometry
Good book on advanced trig
$endgroup$
$begingroup$
That should help, thanks.
$endgroup$
– weno
Dec 5 '18 at 1:14
$begingroup$
Do not hesitate to ask for any exercise in particular! Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:15
$begingroup$
I would, but unless I made any significant progress myself, I don't think anyone will solve that for me. :)
$endgroup$
– weno
Dec 5 '18 at 1:17
$begingroup$
That’s nice but in case of doubt I would happy to check that with you. Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:19
add a comment |
$begingroup$
Some good reference as summary from Wikipedia are
- List of trigonometric identities
and also
- Inverse trigonometric functions
Some exercises given requires only to calculate the value for the functions at some point, other else are more tricky and you need to acquire a deeply understanding of the matter.
Refer also to the related
Reference Request: Book for Trigonometry and Geometry
Good book on advanced trig
$endgroup$
Some good reference as summary from Wikipedia are
- List of trigonometric identities
and also
- Inverse trigonometric functions
Some exercises given requires only to calculate the value for the functions at some point, other else are more tricky and you need to acquire a deeply understanding of the matter.
Refer also to the related
Reference Request: Book for Trigonometry and Geometry
Good book on advanced trig
edited Dec 5 '18 at 1:14
answered Dec 5 '18 at 1:10
gimusigimusi
92.8k84494
92.8k84494
$begingroup$
That should help, thanks.
$endgroup$
– weno
Dec 5 '18 at 1:14
$begingroup$
Do not hesitate to ask for any exercise in particular! Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:15
$begingroup$
I would, but unless I made any significant progress myself, I don't think anyone will solve that for me. :)
$endgroup$
– weno
Dec 5 '18 at 1:17
$begingroup$
That’s nice but in case of doubt I would happy to check that with you. Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:19
add a comment |
$begingroup$
That should help, thanks.
$endgroup$
– weno
Dec 5 '18 at 1:14
$begingroup$
Do not hesitate to ask for any exercise in particular! Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:15
$begingroup$
I would, but unless I made any significant progress myself, I don't think anyone will solve that for me. :)
$endgroup$
– weno
Dec 5 '18 at 1:17
$begingroup$
That’s nice but in case of doubt I would happy to check that with you. Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:19
$begingroup$
That should help, thanks.
$endgroup$
– weno
Dec 5 '18 at 1:14
$begingroup$
That should help, thanks.
$endgroup$
– weno
Dec 5 '18 at 1:14
$begingroup$
Do not hesitate to ask for any exercise in particular! Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:15
$begingroup$
Do not hesitate to ask for any exercise in particular! Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:15
$begingroup$
I would, but unless I made any significant progress myself, I don't think anyone will solve that for me. :)
$endgroup$
– weno
Dec 5 '18 at 1:17
$begingroup$
I would, but unless I made any significant progress myself, I don't think anyone will solve that for me. :)
$endgroup$
– weno
Dec 5 '18 at 1:17
$begingroup$
That’s nice but in case of doubt I would happy to check that with you. Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:19
$begingroup$
That’s nice but in case of doubt I would happy to check that with you. Bye
$endgroup$
– gimusi
Dec 5 '18 at 1:19
add a comment |
$begingroup$
This lecture has been particularly helpful on understanding the subject:
https://academics.utep.edu/Portals/1788/CALCULUS%20MATERIAL/4_7%20INVERSE%20TRIG%20FNS.pdf
$endgroup$
add a comment |
$begingroup$
This lecture has been particularly helpful on understanding the subject:
https://academics.utep.edu/Portals/1788/CALCULUS%20MATERIAL/4_7%20INVERSE%20TRIG%20FNS.pdf
$endgroup$
add a comment |
$begingroup$
This lecture has been particularly helpful on understanding the subject:
https://academics.utep.edu/Portals/1788/CALCULUS%20MATERIAL/4_7%20INVERSE%20TRIG%20FNS.pdf
$endgroup$
This lecture has been particularly helpful on understanding the subject:
https://academics.utep.edu/Portals/1788/CALCULUS%20MATERIAL/4_7%20INVERSE%20TRIG%20FNS.pdf
answered Dec 5 '18 at 3:35
wenoweno
30511
30511
add a comment |
add a comment |
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1
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inverse trigonometric functions is what I would call them
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– Henry Lee
Dec 5 '18 at 1:06
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also a lot of them just require the compound angle formula or some rearrangment to make them a lot easier
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– Henry Lee
Dec 5 '18 at 1:07
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"cyclometric" is the old name for the inverse trig functions. Any basic book should have sections on how to evaluate these.
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– SZN
Dec 5 '18 at 1:11
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these are more simple but a start: tutorial.math.lamar.edu/Extras/AlgebraTrigReview/…
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– Henry Lee
Dec 5 '18 at 1:11
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if you ask specifically about 1 of those questions that you struggle with people will also help
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– Henry Lee
Dec 5 '18 at 1:12