How do you simplify (sin 60)^2 + (cos 60)^2?

1 Answer
George C.
May 25, 2015

(sin 60^o)^2 + (cos 60^o)^2 = 1

In fact, for any angle theta we have sin^2theta + cos^2theta = 1

We can see this geometrically for positive angles less than 90^o (e.g. 60^o) by considering a right angled triangle with angles theta, 90^o - theta and 90^o and hypotenuse of length 1.

By the definitions of sin theta and cos theta, the side opposite the angle theta will be of length sin theta and the side adjacent to the angle theta, opposite the 90^o - theta angle will be of length cos theta.

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