How do you evaluate Sin^2 (pi/9) + Cos^2( pi/9)?

1 Answer
sente
Feb 4, 2016

1

Explanation:

Without even considering the arguments of sine and cosine, there is an identity that for all x, sin^2(x) + cos^2(x) = 1.

One way of seeing that this is true is to consider the unit circle, and note that for any point on the circle with angle theta, cos(theta) is the x-coordinate of that point, and sin(theta) is the y-coordinate. Then, drawing a right triangle with the hypotenuse connecting the origin and the point, we find that the triangle has legs of length cos(theta) and sin(theta), and a hypotenuse of length 1. Applying the Pythagorean theorem gives us the desired result.

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