Solve for all possible values of x where O°≤x≤360°.

Question

tan x = -1/√3
cos x = 1/2

Answer 1

Use the CAST rule to determine the sign of the functions cosine and tangent:

C-quad.4, Cosine >0
A-quad.1, All functions >0
S-quad.2, sin>0
T-quad.3, tan>0

From the given values,
cos(θ)>0 and
tan(θ)<0
Only θ in quad.4 will satisfy both conditions.

Therefore find the reference angle (between 0 and 90°)
t=arctan(1/√3), or
t=arccos(1/2)
and obtain
θ=360-t (4th quadrant).