Answer:
a) 120° +360°k, 150° +360°k, 210° +360°k, 240° +360°k
b) 120°, 150°, 210°, 240°
Explanation:
You want solutions to the equation (2cos(θ) +√3)(2cos(θ) +1) = 0.
Zero product rule
The zero product rule tells you that a product is zero if and only if at least one factor is zero. Here, that means ...
2cos(θ) +√3 = 0 ⇒ cos(θ) = -√3/2
2cos(θ) +1 = 0 ⇒ cos(θ) = -1/2
b. Angles
In the attached figure, the cosine of the angle is the first number of each ordered pair. The angles that correspond to the values of cos(θ) above are ...
120°, 150°, 210°, 240°
a. All angles
The cosine is periodic with period 360°, so "all solutions" will be ...
120° +360°k, 150° +360°k, 210° +360°k, 240° +360°k