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In Unit circle, in second quadrant, why is X taken negative? [duplicate]

When the trig functions moved from the right triangle to the unit circle?Visually stunning math concepts which are easy to explainSolving negative domain trigonometric equations with unit circleWhy $cos(-theta)$ gives positive values while in case of sine it is negative?Why can $(x,y)$ coordinates be defined as $(costheta,sintheta)$ for the unit circle?If trigonometric ratios are just ratios of length of sides, then why do they become negative?Unit Circle - Angles Reflected Across AxisFind the coordinates of the vector in quadrant 4, in terms of $sin(theta)$ and $cos(theta)$. Assume the hypotenuse is equal to 1.Why does the trigonometric Pythagorean theorem works outside the unit circle?Why is the hypotenuse in trig always positive regardless of the quadrant?On Negative Lengths And Positive Hypotenuses In TrigonometryWhy do we choose a unit circle with center at origin to define trigonometric ratios?

0

$begingroup$

This question already has an answer here:

• 
  When the trig functions moved from the right triangle to the unit circle?
  
  3 answers
  
  

Cos theta = base / hypotenuse

Base and hypotenuse are lengths, so they should always be positive.

So why is cos 3π / 4 negative ?

trigonometry

share|cite|improve this question

edited Mar 11 at 21:33

J. W. Tanner

3,2701320

asked Mar 11 at 20:49

arandomguyarandomguy

16017

$endgroup$

marked as duplicate by Blue trigonometry
Users with the  trigonometry badge can single-handedly close trigonometry questions as duplicates and reopen them as needed.

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Mar 11 at 21:07

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Draw or get a computer or a graphics calculator to draw the graph of $y=cos x$ between 0 and $2pi$ radians.
  $endgroup$
  – Martin Hansen
  Mar 11 at 20:59
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Always positive is from original definition, but extensions to all angles of a unit circle needs signed values for x and y.
  $endgroup$
  – herb steinberg
  Mar 11 at 21:03
  

  
  
  
  

add a comment | 

0

$begingroup$

This question already has an answer here:

• 
  When the trig functions moved from the right triangle to the unit circle?
  
  3 answers
  
  

Cos theta = base / hypotenuse

Base and hypotenuse are lengths, so they should always be positive.

So why is cos 3π / 4 negative ?

trigonometry

share|cite|improve this question

edited Mar 11 at 21:33

J. W. Tanner

3,2701320

asked Mar 11 at 20:49

arandomguyarandomguy

16017

$endgroup$

marked as duplicate by Blue trigonometry
Users with the  trigonometry badge can single-handedly close trigonometry questions as duplicates and reopen them as needed.

StackExchange.ready(function()
if (StackExchange.options.isMobile) return;

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var $hover = $(this).addClass('hover-bound'),
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StackExchange.helpers.removeMessages();

);
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Mar 11 at 21:07

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Draw or get a computer or a graphics calculator to draw the graph of $y=cos x$ between 0 and $2pi$ radians.
  $endgroup$
  – Martin Hansen
  Mar 11 at 20:59
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Always positive is from original definition, but extensions to all angles of a unit circle needs signed values for x and y.
  $endgroup$
  – herb steinberg
  Mar 11 at 21:03
  

  
  
  
  

add a comment | 

$begingroup$

This question already has an answer here:

• 
  When the trig functions moved from the right triangle to the unit circle?
  
  3 answers
  
  

Cos theta = base / hypotenuse

Base and hypotenuse are lengths, so they should always be positive.

So why is cos 3π / 4 negative ?

trigonometry

share|cite|improve this question

edited Mar 11 at 21:33

J. W. Tanner

3,2701320

asked Mar 11 at 20:49

arandomguyarandomguy

16017

$endgroup$

share|cite|improve this question

edited Mar 11 at 21:33

J. W. Tanner

3,2701320

asked Mar 11 at 20:49

arandomguyarandomguy

16017

share|cite|improve this question

edited Mar 11 at 21:33

J. W. Tanner

3,2701320

asked Mar 11 at 20:49

arandomguyarandomguy

16017

edited Mar 11 at 21:33

J. W. Tanner

3,2701320

edited Mar 11 at 21:33

J. W. Tanner

3,2701320

asked Mar 11 at 20:49

arandomguyarandomguy

16017

asked Mar 11 at 20:49

arandomguyarandomguy

16017

1 Answer
1

active

oldest

votes

0

$begingroup$

I pinched this from another post, but it may help;

I think if you look at this animation and think about it long enough, you'll understand:

• Why circles and right-angle triangles and angles are all related


• Why sine is opposite over hypotenuse and so on


• Why cosine is simply sine but offset by $pi/2$ radians

share|cite|improve this answer

answered Mar 11 at 21:04

Martin HansenMartin Hansen

56214

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You should link to the post from which you took this diagram; chances are good that the question and/or other answers could be useful to OP. (Also, if you are not the original creator of the diagram, credit should be given.)
  $endgroup$
  – Blue
  Mar 11 at 21:17
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Blue : It's from a community wiki, and happy to link to the post. It does not add anything more, although its a very long and visually stunning romp through beautiful maths - but not relevant to the question asked here. Link math.stackexchange.com/questions/733754/…
  $endgroup$
  – Martin Hansen
  Mar 11 at 21:24
  

  
  
  
  

add a comment | 

0

$begingroup$

I pinched this from another post, but it may help;

I think if you look at this animation and think about it long enough, you'll understand:

• Why circles and right-angle triangles and angles are all related


• Why sine is opposite over hypotenuse and so on


• Why cosine is simply sine but offset by $pi/2$ radians

share|cite|improve this answer

answered Mar 11 at 21:04

Martin HansenMartin Hansen

56214

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You should link to the post from which you took this diagram; chances are good that the question and/or other answers could be useful to OP. (Also, if you are not the original creator of the diagram, credit should be given.)
  $endgroup$
  – Blue
  Mar 11 at 21:17
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Blue : It's from a community wiki, and happy to link to the post. It does not add anything more, although its a very long and visually stunning romp through beautiful maths - but not relevant to the question asked here. Link math.stackexchange.com/questions/733754/…
  $endgroup$
  – Martin Hansen
  Mar 11 at 21:24
  

  
  
  
  

add a comment | 

0

$begingroup$

I pinched this from another post, but it may help;

I think if you look at this animation and think about it long enough, you'll understand:

• Why circles and right-angle triangles and angles are all related


• Why sine is opposite over hypotenuse and so on


• Why cosine is simply sine but offset by $pi/2$ radians

share|cite|improve this answer

answered Mar 11 at 21:04

Martin HansenMartin Hansen

56214

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  You should link to the post from which you took this diagram; chances are good that the question and/or other answers could be useful to OP. (Also, if you are not the original creator of the diagram, credit should be given.)
  $endgroup$
  – Blue
  Mar 11 at 21:17
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  @Blue : It's from a community wiki, and happy to link to the post. It does not add anything more, although its a very long and visually stunning romp through beautiful maths - but not relevant to the question asked here. Link math.stackexchange.com/questions/733754/…
  $endgroup$
  – Martin Hansen
  Mar 11 at 21:24
  

  
  
  
  

add a comment | 

$begingroup$

I pinched this from another post, but it may help;

I think if you look at this animation and think about it long enough, you'll understand:

• Why circles and right-angle triangles and angles are all related


• Why sine is opposite over hypotenuse and so on


• Why cosine is simply sine but offset by $pi/2$ radians

share|cite|improve this answer

answered Mar 11 at 21:04

Martin HansenMartin Hansen

56214

$endgroup$

share|cite|improve this answer

answered Mar 11 at 21:04

Martin HansenMartin Hansen

56214

answered Mar 11 at 21:04

Martin HansenMartin Hansen

56214

answered Mar 11 at 21:04

Martin HansenMartin Hansen

56214