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Solve for all possible values of x where O°≤x≤360°.
tan x = -1/√3
cos x = 1/2

  • Math -

    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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