Question

How do you find the exact value of sec θ if sin θ = -15/17 and 180 < θ < 270?

Answer 1

For $180^\circ<\theta<270^\circ$, we expect to have $\cos\theta<0$. Then if $\sin\theta=-\dfrac{15}{17}$, we have

$cos^2\theta+\sin^2\theta=1\implies\cos\theta=-\sqrt{1-\sin^2\theta}=-\dfrac8{17}$

$\implies\sec\theta=\boxed{-\dfrac{17}8}$