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I know that sine is the ratio of the perpendicular to the hypotenuse of an acute angle. Similarly cosine is the ratio of the base and hypotenuse .
But now I found that there is sine and cosine of an angle over 90 degrees or negative degrees . I do not understand how they can determine the value of these sine and cosine . I have heard about the unit circle , and I find it is not convincing to determined the value of sine and cosine just by looking at the picture . I mean , is there any others method like using equations or theorems to calculate the cosine of an over 90 degrees?