Question

Solve on the interval [0, 2pi): 1 + cos θ = 1/2

Answer 1

subtract 1 on both sides

Answer 2

\[\cos(\theta)=\frac{1}{2}-1 \\ \cos(\theta)=\frac{-1}{2}\]
now use handy dandy unit circle
find theta such that the x-coordinates on your unit circle are -1/2

Answer 3

theta = x.
1 + cos x = 1/2.
cos x = -1/2.
cos x = 1/2 at pi/3.
cos x = -1/2 occurs in quadrants 2 and 3.
pi/3 be the reference angle.
So pi+pi/3 = 4pi/3 and pi - pi/3 = 2pi/3.
So B is the answer.

Answer 4

is this right?

Answer 5

yes B is the right answer

Answer 6

Thank you!

Answer 7

np