Math
posted by Kate on .
Solve for all possible values of x where O°≤x≤360°.
tan x = 1/√3
cos x = 1/2

Use the CAST rule to determine the sign of the functions cosine and tangent:
Cquad.4, Cosine >0
Aquad.1, All functions >0
Squad.2, sin>0
Tquad.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=360t (4th quadrant).