select all angle measures for which $cos\theta=\frac{1}{2}$. -120° -60° 120° 600° 660° done
select all angle measures for which $cos\theta=\frac{1}{2}$. -120° -60° 120° 600° 660° done
Answer
Explanation:
Step1: Recall cosine values
We know that $\cos\theta=\frac{1}{2}$ when $\theta = 60^{\circ}+ 360^{\circ}n$ or $\theta=- 60^{\circ}+360^{\circ}n$, where $n\in\mathbb{Z}$.
Step2: Check each option
- For $\theta=-120^{\circ}$, $\cos(-120^{\circ})=-\frac{1}{2}$.
- For $\theta = - 60^{\circ}$, $\cos(-60^{\circ})=\frac{1}{2}$.
- For $\theta = 120^{\circ}$, $\cos(120^{\circ})=-\frac{1}{2}$.
- For $\theta = 600^{\circ}$, $\theta=360^{\circ}+240^{\circ}$, $\cos(600^{\circ})=\cos(240^{\circ})=-\frac{1}{2}$.
- For $\theta = 660^{\circ}$, $\theta = 360^{\circ}+300^{\circ}$, $\cos(660^{\circ})=\cos(300^{\circ})=\cos(-60^{\circ})=\frac{1}{2}$.
Answer:
- B. $-60^{\circ}$
- E. $660^{\circ}$