Question

GIVING MEDALS
solve the equation cosx=-1/2 if 0 degrees <=x<=360 degrees
a. 135, 225 degrees
b. 210, 330 degrees
c. 150, 210 degrees
d. 120, 240 degrees

Answer 1

Alternately u can do this....
I assume you mean 0 degree ≤ x ≤ 360 degree

sec x = −2
1/cos x = −2
cosx = −1/2 -----> this you should know

x = 120°
or
x = 360° − 120° = 240°

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If you're not too sure about all values of x where cosx = −1/2, you should at least know all the important in first quadrant. So you can find reference angle in first quadrant where
cos θ = 1/2 ----> θ = 60°

Angle x in quadrant II with reference angle θ ----> x = 180° − θ
Angle x in quadrant III with reference angle θ ----> x = 180° + θ
Angle x in quadrant IV with reference angle θ ----> x = 360° − θ

Since cos x = −1/2 < 0, then x is in quadrant II or III
x = 180° − θ = 180° − 60° = 120°
x = 180° + θ = 180° + 60° = 240°