## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$\dfrac{\sqrt 3}{2}$
Let us consider: $f(\theta)=\sin \theta$ When $\theta=60^{\circ}$, then $2 \theta=2 (60^{\circ})=124^{\circ}$ We know from the unit circle that $\sin (120^{\circ})=\sin (\dfrac{2\pi}{3})=\dfrac{\sqrt 3}{2}$ Thus, we have: $f(2\theta)=\sin (120^{\circ}) \\=\sin\dfrac{2\pi}{3} \\ =\dfrac{\sqrt 3}{2}$