Posted by **Kate** on Sunday, July 17, 2011 at 10:29am.

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

tan x = -1/√3

cos x = 1/2

- Math -
**MathMate**, Sunday, July 17, 2011 at 1:19pm
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).

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