This question already has an answer here:

Cos theta = base / hypotenuse

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

So why is cos 3π / 4 negative ?


marked as duplicate by Blue trigonometry Mar 11 at 21:07

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  • $\begingroup$ Draw or get a computer or a graphics calculator to draw the graph of $y=cos x$ between 0 and $2\pi$ 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

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

circle trig animation

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
  • $\begingroup$ 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

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