# How do you prove sin theta = 0 and cos theta = 1?

Jun 29, 2016

If $\sin \theta = 0 , \cos \theta = \pm 1$

#### Explanation:

I am answering the question "If $\sin \theta = 0$, prove $\cos \theta = \pm 1$?"

Use $\cos \theta = \pm \sqrt{1 - {\sin}^{2} \theta} = \pm \sqrt{1 - 0} = \pm 1.$

The general solution of $\sin \theta = 0$ is

$n \pi , n = 0 , + = 1 , \pm 2 , \pm 3 , \ldots$

So $\cos \theta = \cos n \pi = {\left(- 1\right)}^{n}$

=1, for $n = 0 , \pm 2 , \pm 4. \pm 6 , . .$.and

$= - 1$, for $n = \pm 1 , \pm 3 , \pm 5 , \ldots$.