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 trigonometric function

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

Step2: Substitute the values into the expression

$$
LATEXBLOCK0
$$

Answer:

A. $\cos60^{\circ}+\cos120^{\circ}-\cos240^{\circ}+\cos300^{\circ}=1$