Question

Given cos θ=-15/17 and 180°<θ<270° , find the exact value of each expression. sin θ/2

Answer 1

Answer:
`\sqrt{(1-(-15/17))/(2)}`

Explanation:

Note that
`180^(\circ) < \theta < 270^(\circ) \implies 90^(\circ) < (\theta)/(2) < 135^(\circ) \implies \sin (\theta)/(2) > 0`.

Using the half-angle formula
`\sin (\theta)/(2)=\sqrt{(1-\cos \theta)/(2)}`,

`\sin (\theta)/(2)=\sqrt{(1-(-15/17))/(2)}=(4√(17))/(17)`