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

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Answer 1 · 2016-06-29T03:35:26

If $sin theta = 0, cos theta = +-1$

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

Use $cos theta = +-sqrt(1-sin^2theta)=+-sqrt(1-0)=+-1.$

The general solution of $sin theta = 0$ is

$npi, n=0, +=1, +-2, +-3, ...$

So $cos theta=cos npi=(-1)^n$

=1, for $n=0, +-2, +-4.+-6, ..$ .and

$=-1$ , for $n=+-1, +-3, +-5,...$ .

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