QuestionIf $\theta=240^{\circ}$, find the exact value of each expression below. (a) $2 \cos \theta=$ $\square$ (b) $\quad \cos \frac{\theta}{2}=$ $\square$ (c) $\cos ^{2} \theta=$ $\square$

Studdy Solution
Calculate $\cos^2 \theta$:
$$\cos^2 240^\circ = \left(\cos 240^\circ\right)^2$$
$$= \left(-\frac{1}{2}\right)^2$$
$$= \frac{1}{4}$$
The exact values are: (a) $2 \cos \theta = -1$ (b) $\cos \frac{\theta}{2} = -\frac{1}{2}$ (c) $\cos^2 \theta = \frac{1}{4}$