Does Niven's theorem apply to cosine function?

Question

Niven's theorem says that if $\theta$ is a rational multiple of $\pi$ and $\sin \theta$ is rational then $\sin \theta = 0, -\frac12, \frac12, -1, 1$. But is this theorem applicable to cosine function?

Answer 1

Yes because $\cos\theta=\sin(\frac\pi 2-\theta)$.

Answer 2

The theorem also applies to the other trigonometric functions. The sine and cosine have only three rational values: 0, 1/2, and 1; the secant and cosecant have only two rational values: 1 and 2; and the tangent and cotangent have only two rational values: 0 and 1.

Reference https://en.wikipedia.org/wiki/Niven%27s_theorem

Answer 3

Yes. Use fundamental formula $sin^2(x)+cos^2(x)=1$ or trigonometric circle and you can just change sin with cos and viceversa.Think that $sin (x)= cos (\frac{\pi}{2}-x)$ and $cos(x)=sin (\frac{\pi}{2}-x)$.