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Sine-cosine square identity

One trigonometric identity states that for any angle :

For a unit triangle (one where the hypotenuse has length 1), the lengths of the two other sides correspond to the sine and cosine of the angle .

In other words, the side opposite to angle has length , and the side adjacent to angle has length .

From the pythagorean theorem, we know that for any right triangle with sides of lengths and , and hypotenuse of length :

In this case:

So we can substitute these values into the pythagorean theorem!

which is otherwise written as: