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This question already has an answer here:

How does the unit circle work for trigonometric ratios of obtuse angles? I know that the x coordinate is cos(θ) and the y coordinate is sin(θ). But I understand these in context of only acute angles? I don't understand why the unit circle definition works for other than acute angles? Somebody please provide me some good intuition.

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marked as duplicate by David K, YuiTo Cheng, Lee David Chung Lin, hardmath, Aqua Jul 16 at 5:08

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Take the ratios $x/r$ and $y/r$ as the defintions of cosine and sine. Note that the definitions you already know for acute angles (“opposite side/hypotenuse” etc) then become a special case.

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    $\begingroup$ I would prefer this to be reintroduced as defintions in high school for all angles when students get to coordinate geometry. $\endgroup$ – Mathemagical Nov 9 '17 at 8:05

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