Question

find all angles (in degrees) that satisfy the following equation.
2 cos(α) - √3 = 0

select the correct choice below and, if necessary, fill in the answer boxes to complete your choice.
a. the solution set is {α | α = □° + k□° or α = □° + k□°}, where k is any integer.
(use angle measures greater than 0 and less than or equal to 360. type integers or fractions.)
b. the solution set is {α | α = □° + k□°}, where k is any integer.
(use angle measures greater than 0 and less than or equal to 360. type integers or fractions.)
c. there is no solution.

Explanation:

Step1: Isolate cos(u)

$2\cos(u) = \sqrt{3} \implies \cos(u) = \frac{\sqrt{3}}{2}$

Step2: Find reference angle

$\cos(30^\circ) = \frac{\sqrt{3}}{2}$, so reference angle is $30^\circ$.

Step3: Identify quadrants

Cosine positive in Q1/Q4: $u=30^\circ$ (Q1), $u=360^\circ-30^\circ=330^\circ$ (Q4).

Step4: General solution

Add $360^\circ k$ (period of cosine).

Answer:

A. The solution set is $\{ u \mid u = 30^\circ + k360^\circ \text{ or } u = 330^\circ + k360^\circ \}$, where k is any integer.