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,...#.