Question #ac2da

1 Answer
sente
Aug 10, 2016

No such theta exists.

Explanation:

It is an identity that cos^2(theta) + sin^2(theta) = 1 for all theta, thus no theta will result in the given equality.

In the real numbers, there is also the reasoning that
-1<=cos(theta)<=1 and -1<=sin(theta)<=1
=>
0 <= cos^2(theta) <= 1 and 0<=sin^2(theta)<=1.

Then, even if we allow different angles, for any theta, gamma in RR (the real numbers):

cos^2(theta)+sin^2(gamma) <= 1+1 = 2

Even if we allow for complex arguments, however, which allow for greater values of sine and cosine, the original identity still holds, meaning there is still no theta fulfilling cos^2(theta)+sin^2(theta)=3.

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