Cos theta = base / hypotenuse
Base and hypotenuse are lengths, so they should always be positive.
So why is cos 3π / 4 negative ?
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Draw or get a computer or a graphics calculator to draw the graph of $y=cos x$ between 0 and $2\pi$ radians. – Martin Hansen Mar 11 '19 at 20:59
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Always positive is from original definition, but extensions to all angles of a unit circle needs signed values for x and y. – herb steinberg Mar 11 '19 at 21:03
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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
Martin Hansen
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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.) – Blue Mar 11 '19 at 21:17
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@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 https://math.stackexchange.com/questions/733754/visually-stunning-math-concepts-which-are-easy-to-explain – Martin Hansen Mar 11 '19 at 21:24