Question

rewrite the expression in terms of the given angles reference angle; then evaluate the result. write the exact answer. do not round. cos(-240°)

Explanation:

Step1: Find the reference angle

The angle $\theta=- 240^{\circ}$. First, find a positive - coterminal angle. Add $360^{\circ}$ to $-240^{\circ}$: $\alpha=-240^{\circ}+360^{\circ}=120^{\circ}$. Since $120^{\circ}$ is in the second quadrant, the reference angle $\theta_{r}=180^{\circ}-120^{\circ}=60^{\circ}$.

Step2: Determine the sign of the cosine function

The cosine function has the property $\cos(-\theta)=\cos\theta$. Also, in the second quadrant, $\cos\theta<0$. So, $\cos(-240^{\circ})=\cos(120^{\circ})=-\cos(60^{\circ})$.

Step3: Evaluate the cosine of the reference angle

We know that $\cos(60^{\circ})=\frac{1}{2}$. So, $-\cos(60^{\circ})=-\frac{1}{2}$.

Answer:

$-\frac{1}{2}$