What is the geometric interpretation of the value of the secant and cosecant of an angle?
9
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I am confused about what is the geometric representation and interpretation of the secant and cosecant of an angle. I understand how to calculate them but I do not know what they mean, geometrically.
geometry trigonometry terminology circle triangle
asked Dec 12 '16 at 23:44
yoyo_funyoyo_fun
393313
$endgroup$
add a comment |
9
$begingroup$
I am confused about what is the geometric representation and interpretation of the secant and cosecant of an angle. I understand how to calculate them but I do not know what they mean, geometrically.
geometry trigonometry terminology circle triangle
asked Dec 12 '16 at 23:44
yoyo_funyoyo_fun
393313
$endgroup$
$begingroup$
I doubt there is really any.. they're just there to help you later on in future math courses; e.g. the derivative (calculus term) of the tangent function is secant squared.
$endgroup$
– pie314271
Dec 12 '16 at 23:48
$begingroup$
@pie314271 Do you still have doubts after seeing the diagrams below?
$endgroup$
– Théophile
Dec 13 '16 at 0:16
$begingroup$
@Théophile: I was thinking that he was referring to the usages of secant/cosecant (e.g. $e^{ix}=cos x+isin x$). Of course there's that, but based on the OP's response you're probably right.
$endgroup$
– pie314271
Dec 13 '16 at 0:34
add a comment |
9
9
9
2
$begingroup$
I am confused about what is the geometric representation and interpretation of the secant and cosecant of an angle. I understand how to calculate them but I do not know what they mean, geometrically.
geometry trigonometry terminology circle triangle
asked Dec 12 '16 at 23:44
yoyo_funyoyo_fun
393313
$endgroup$
I am confused about what is the geometric representation and interpretation of the secant and cosecant of an angle. I understand how to calculate them but I do not know what they mean, geometrically.
geometry trigonometry terminology circle triangle
geometry trigonometry terminology circle triangle
asked Dec 12 '16 at 23:44
yoyo_funyoyo_fun
393313
asked Dec 12 '16 at 23:44
yoyo_funyoyo_fun
393313
asked Dec 12 '16 at 23:44
yoyo_funyoyo_fun
393313
asked Dec 12 '16 at 23:44
yoyo_funyoyo_fun
393313
asked Dec 12 '16 at 23:44
yoyo_funyoyo_fun
393313
393313
$begingroup$
I doubt there is really any.. they're just there to help you later on in future math courses; e.g. the derivative (calculus term) of the tangent function is secant squared.
$endgroup$
– pie314271
Dec 12 '16 at 23:48
$begingroup$
@pie314271 Do you still have doubts after seeing the diagrams below?
$endgroup$
– Théophile
Dec 13 '16 at 0:16
$begingroup$
@Théophile: I was thinking that he was referring to the usages of secant/cosecant (e.g. $e^{ix}=cos x+isin x$). Of course there's that, but based on the OP's response you're probably right.
$endgroup$
– pie314271
Dec 13 '16 at 0:34
add a comment |
$begingroup$
I doubt there is really any.. they're just there to help you later on in future math courses; e.g. the derivative (calculus term) of the tangent function is secant squared.
$endgroup$
– pie314271
Dec 12 '16 at 23:48
$begingroup$
@pie314271 Do you still have doubts after seeing the diagrams below?
$endgroup$
– Théophile
Dec 13 '16 at 0:16
$begingroup$
@Théophile: I was thinking that he was referring to the usages of secant/cosecant (e.g. $e^{ix}=cos x+isin x$). Of course there's that, but based on the OP's response you're probably right.
$endgroup$
– pie314271
Dec 13 '16 at 0:34
$begingroup$
I doubt there is really any.. they're just there to help you later on in future math courses; e.g. the derivative (calculus term) of the tangent function is secant squared.
$endgroup$
– pie314271
Dec 12 '16 at 23:48
$begingroup$
I doubt there is really any.. they're just there to help you later on in future math courses; e.g. the derivative (calculus term) of the tangent function is secant squared.
$endgroup$
– pie314271
Dec 12 '16 at 23:48
$begingroup$
@pie314271 Do you still have doubts after seeing the diagrams below?
$endgroup$
– Théophile
Dec 13 '16 at 0:16
$begingroup$
@pie314271 Do you still have doubts after seeing the diagrams below?
$endgroup$
– Théophile
Dec 13 '16 at 0:16
$begingroup$
@Théophile: I was thinking that he was referring to the usages of secant/cosecant (e.g. $e^{ix}=cos x+isin x$). Of course there's that, but based on the OP's response you're probably right.
$endgroup$
– pie314271
Dec 13 '16 at 0:34
$begingroup$
@Théophile: I was thinking that he was referring to the usages of secant/cosecant (e.g. $e^{ix}=cos x+isin x$). Of course there's that, but based on the OP's response you're probably right.
$endgroup$
– pie314271
Dec 13 '16 at 0:34
add a comment |
2 Answers
2
active
oldest
votes
10
$begingroup$
In the usual terms or geometric representation of cos and sin on the unit circle in terms of some angle $theta$ you can also get a 'geometric representation' of sec and cosec here also. See the image below.
answered Dec 12 '16 at 23:55
RumplestillskinRumplestillskin
1,059421
$endgroup$
$begingroup$
I think the way of looking at it that is shown in Wikipedia's article on trigonometric functions is better. See my posted answer.
$endgroup$
– Michael Hardy
Dec 13 '16 at 0:07
$begingroup$
@MichaelHardy Why do prefer the other diagram?
$endgroup$
– Théophile
Dec 13 '16 at 0:15
$begingroup$
@Théophile : I may actually have to collect my thoughts on this in order to write as short an answer as the question deserves.
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:08
$begingroup$
@Théophile : One reason is that it allows a good explanation of why the tangent and secant are positive in certain quadrants and negative in certain other quadrants. $qquad$
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:09
1
$begingroup$
@MichaelHardy “If I had had more time, I would’ve written a shorter article.” — Mark Twain.
$endgroup$
– amd
Dec 13 '16 at 7:11
|
show 2 more comments
9
$begingroup$
${{{{{{{{{{{{{{{{{{{{qquad}}}}}}}}}}}}}}}}}}}}$
answered Dec 13 '16 at 0:04
Michael HardyMichael Hardy
1
$endgroup$
1
$begingroup$
This (rather than the other diagram) is the way I was taught long, long ago.
$endgroup$
– amd
Dec 13 '16 at 7:12
add a comment |
Your Answer
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2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
10
$begingroup$
In the usual terms or geometric representation of cos and sin on the unit circle in terms of some angle $theta$ you can also get a 'geometric representation' of sec and cosec here also. See the image below.
answered Dec 12 '16 at 23:55
RumplestillskinRumplestillskin
1,059421
$endgroup$
$begingroup$
I think the way of looking at it that is shown in Wikipedia's article on trigonometric functions is better. See my posted answer.
$endgroup$
– Michael Hardy
Dec 13 '16 at 0:07
$begingroup$
@MichaelHardy Why do prefer the other diagram?
$endgroup$
– Théophile
Dec 13 '16 at 0:15
$begingroup$
@Théophile : I may actually have to collect my thoughts on this in order to write as short an answer as the question deserves.
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:08
$begingroup$
@Théophile : One reason is that it allows a good explanation of why the tangent and secant are positive in certain quadrants and negative in certain other quadrants. $qquad$
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:09
1
$begingroup$
@MichaelHardy “If I had had more time, I would’ve written a shorter article.” — Mark Twain.
$endgroup$
– amd
Dec 13 '16 at 7:11
|
show 2 more comments
10
$begingroup$
In the usual terms or geometric representation of cos and sin on the unit circle in terms of some angle $theta$ you can also get a 'geometric representation' of sec and cosec here also. See the image below.
answered Dec 12 '16 at 23:55
RumplestillskinRumplestillskin
1,059421
$endgroup$
$begingroup$
I think the way of looking at it that is shown in Wikipedia's article on trigonometric functions is better. See my posted answer.
$endgroup$
– Michael Hardy
Dec 13 '16 at 0:07
$begingroup$
@MichaelHardy Why do prefer the other diagram?
$endgroup$
– Théophile
Dec 13 '16 at 0:15
$begingroup$
@Théophile : I may actually have to collect my thoughts on this in order to write as short an answer as the question deserves.
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:08
$begingroup$
@Théophile : One reason is that it allows a good explanation of why the tangent and secant are positive in certain quadrants and negative in certain other quadrants. $qquad$
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:09
1
$begingroup$
@MichaelHardy “If I had had more time, I would’ve written a shorter article.” — Mark Twain.
$endgroup$
– amd
Dec 13 '16 at 7:11
|
show 2 more comments
10
10
10
$begingroup$
In the usual terms or geometric representation of cos and sin on the unit circle in terms of some angle $theta$ you can also get a 'geometric representation' of sec and cosec here also. See the image below.
answered Dec 12 '16 at 23:55
RumplestillskinRumplestillskin
1,059421
$endgroup$
In the usual terms or geometric representation of cos and sin on the unit circle in terms of some angle $theta$ you can also get a 'geometric representation' of sec and cosec here also. See the image below.
answered Dec 12 '16 at 23:55
RumplestillskinRumplestillskin
1,059421
answered Dec 12 '16 at 23:55
RumplestillskinRumplestillskin
1,059421
answered Dec 12 '16 at 23:55
RumplestillskinRumplestillskin
1,059421
answered Dec 12 '16 at 23:55
RumplestillskinRumplestillskin
1,059421
1,059421
$begingroup$
I think the way of looking at it that is shown in Wikipedia's article on trigonometric functions is better. See my posted answer.
$endgroup$
– Michael Hardy
Dec 13 '16 at 0:07
$begingroup$
@MichaelHardy Why do prefer the other diagram?
$endgroup$
– Théophile
Dec 13 '16 at 0:15
$begingroup$
@Théophile : I may actually have to collect my thoughts on this in order to write as short an answer as the question deserves.
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:08
$begingroup$
@Théophile : One reason is that it allows a good explanation of why the tangent and secant are positive in certain quadrants and negative in certain other quadrants. $qquad$
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:09
1
$begingroup$
@MichaelHardy “If I had had more time, I would’ve written a shorter article.” — Mark Twain.
$endgroup$
– amd
Dec 13 '16 at 7:11
|
show 2 more comments
$begingroup$
I think the way of looking at it that is shown in Wikipedia's article on trigonometric functions is better. See my posted answer.
$endgroup$
– Michael Hardy
Dec 13 '16 at 0:07
$begingroup$
@MichaelHardy Why do prefer the other diagram?
$endgroup$
– Théophile
Dec 13 '16 at 0:15
$begingroup$
@Théophile : I may actually have to collect my thoughts on this in order to write as short an answer as the question deserves.
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:08
$begingroup$
@Théophile : One reason is that it allows a good explanation of why the tangent and secant are positive in certain quadrants and negative in certain other quadrants. $qquad$
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:09
1
$begingroup$
@MichaelHardy “If I had had more time, I would’ve written a shorter article.” — Mark Twain.
$endgroup$
– amd
Dec 13 '16 at 7:11
$begingroup$
I think the way of looking at it that is shown in Wikipedia's article on trigonometric functions is better. See my posted answer.
$endgroup$
– Michael Hardy
Dec 13 '16 at 0:07
$begingroup$
I think the way of looking at it that is shown in Wikipedia's article on trigonometric functions is better. See my posted answer.
$endgroup$
– Michael Hardy
Dec 13 '16 at 0:07
$begingroup$
@MichaelHardy Why do prefer the other diagram?
$endgroup$
– Théophile
Dec 13 '16 at 0:15
$begingroup$
@MichaelHardy Why do prefer the other diagram?
$endgroup$
– Théophile
Dec 13 '16 at 0:15
$begingroup$
@Théophile : I may actually have to collect my thoughts on this in order to write as short an answer as the question deserves.
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:08
$begingroup$
@Théophile : I may actually have to collect my thoughts on this in order to write as short an answer as the question deserves.
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:08
$begingroup$
@Théophile : One reason is that it allows a good explanation of why the tangent and secant are positive in certain quadrants and negative in certain other quadrants. $qquad$
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:09
$begingroup$
@Théophile : One reason is that it allows a good explanation of why the tangent and secant are positive in certain quadrants and negative in certain other quadrants. $qquad$
$endgroup$
– Michael Hardy
Dec 13 '16 at 1:09
1
1
$begingroup$
@MichaelHardy “If I had had more time, I would’ve written a shorter article.” — Mark Twain.
$endgroup$
– amd
Dec 13 '16 at 7:11
$begingroup$
@MichaelHardy “If I had had more time, I would’ve written a shorter article.” — Mark Twain.
$endgroup$
– amd
Dec 13 '16 at 7:11
|
show 2 more comments
9
$begingroup$
${{{{{{{{{{{{{{{{{{{{qquad}}}}}}}}}}}}}}}}}}}}$
answered Dec 13 '16 at 0:04
Michael HardyMichael Hardy
1
$endgroup$
1
$begingroup$
This (rather than the other diagram) is the way I was taught long, long ago.
$endgroup$
– amd
Dec 13 '16 at 7:12
add a comment |
9
$begingroup$
${{{{{{{{{{{{{{{{{{{{qquad}}}}}}}}}}}}}}}}}}}}$
answered Dec 13 '16 at 0:04
Michael HardyMichael Hardy
1
$endgroup$
1
$begingroup$
This (rather than the other diagram) is the way I was taught long, long ago.
$endgroup$
– amd
Dec 13 '16 at 7:12
add a comment |
9
9
9
$begingroup$
${{{{{{{{{{{{{{{{{{{{qquad}}}}}}}}}}}}}}}}}}}}$
answered Dec 13 '16 at 0:04
Michael HardyMichael Hardy
1
$endgroup$
${{{{{{{{{{{{{{{{{{{{qquad}}}}}}}}}}}}}}}}}}}}$
answered Dec 13 '16 at 0:04
Michael HardyMichael Hardy
1
answered Dec 13 '16 at 0:04
Michael HardyMichael Hardy
1
answered Dec 13 '16 at 0:04
Michael HardyMichael Hardy
1
answered Dec 13 '16 at 0:04
Michael HardyMichael Hardy
1
1
1
$begingroup$
This (rather than the other diagram) is the way I was taught long, long ago.
$endgroup$
– amd
Dec 13 '16 at 7:12
add a comment |
1
$begingroup$
This (rather than the other diagram) is the way I was taught long, long ago.
$endgroup$
– amd
Dec 13 '16 at 7:12
1
1
$begingroup$
This (rather than the other diagram) is the way I was taught long, long ago.
$endgroup$
– amd
Dec 13 '16 at 7:12
$begingroup$
This (rather than the other diagram) is the way I was taught long, long ago.
$endgroup$
– amd
Dec 13 '16 at 7:12
add a comment |
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$begingroup$
I doubt there is really any.. they're just there to help you later on in future math courses; e.g. the derivative (calculus term) of the tangent function is secant squared.
$endgroup$
– pie314271
Dec 12 '16 at 23:48
$begingroup$
@pie314271 Do you still have doubts after seeing the diagrams below?
$endgroup$
– Théophile
Dec 13 '16 at 0:16
$begingroup$
@Théophile: I was thinking that he was referring to the usages of secant/cosecant (e.g. $e^{ix}=cos x+isin x$). Of course there's that, but based on the OP's response you're probably right.
$endgroup$
– pie314271
Dec 13 '16 at 0:34