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Artyom0805 [142]
3 years ago
6

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

Mathematics
1 answer:
AnnyKZ [126]3 years ago
7 0

For 180^\circ, we expect to have \cos\theta. 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}

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