Question

find the exact value of \\( \cos 60^{\circ}+\cos 120^{\circ}+\cos 240^{\circ}+\cos 300^{\circ} \\)

select the correct choice below and fill in any answer boxes in your choice

a. \\( \cos 60^{\circ}+\cos 120^{\circ}+\cos 240^{\circ}+\cos 300^{\circ}= \\)
(type an exact answer, using radicals as needed )

b. the answer is undefined

Explanation:

Step1: Find the value of each cosine term

• $\cos60^{\circ}=\frac{1}{2}$
• $\cos120^{\circ}=\cos(180^{\circ} - 60^{\circ})=-\cos60^{\circ}=-\frac{1}{2}$
• $\cos240^{\circ}=\cos(180^{\circ}+60^{\circ})=-\cos60^{\circ}=-\frac{1}{2}$
• $\cos300^{\circ}=\cos(360^{\circ}-60^{\circ})=\cos60^{\circ}=\frac{1}{2}$

Step2: Sum up the values

$$
LATEXBLOCK0
$$

Answer:

$\cos60^{\circ}+\cos120^{\circ}+\cos240^{\circ}+\cos300^{\circ}=0$