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=-(15)/(17)`, we have

`cos^2\theta+\sin^2\theta=1\implies\cos\theta=-√(1-\sin^2\theta)=-\frac8{17}`

`\implies\sec\theta=\boxed{-\frac{17}8}`