Question

Use the half angle identity to find the exact value of the trigonomic expression. given 0

Answer 1

Given a right angle triangle:

we need to find the measure of the angle θ

As shown:

The opposite side to the angle θ = 24

The adjacent side to the angle θ = 45

So,

`\begin{gathered} \tan \theta=(opposite)/(adjacent)=(24)/(45) \\ \\ \theta=\tan ^(-1)(24)/(45)=28.0725 \\ \\ \sin (\theta)/(2)=\sin (28.0725)/(2)=\sin 14.036=0.2425 \end{gathered}`

so, the answer will be sin θ/2 = 0.2425