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If sin theta = 3/4 and cos theta is negative find csc theta and cot theta

User Prada
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Recall that


\cos^2\theta+\sin^2\theta=1\implies\cos\theta=\pm√(1-\sin^2\theta)

But we're specifically told that cosine is negative, so we take the negative root above, and then


\cos\theta=-√(1-\left(\frac34\right)^2)=-\frac{\sqrt7}4

Now,


\csc\theta=\frac1{\sin\theta}=\frac43


\cot\theta=(\cos\theta)/(\sin\theta)=-\frac{\sqrt7}3

User Ikhsan Assaat
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