we know that
[tex]cos\theta=-\frac{\sqrt{3}}{2}[/tex]
and the domain of angle θ is the interval
[tex](pi,\frac{3pi}{2})[/tex]
that means
The angle θ lies on the III quadrant
the value of sine is negative
the value of the tangent is positive
[tex]\begin{gathered} x=cos^{-1}(\frac{\sqrt{3}}{2}) \\ x=30\text{ degrees} \end{gathered}[/tex]
the angle theta is equal to
θ=180+30=210 degrees=7pi/6 radians
see the figure below to better understand
Find out the value of sin
sinθ=-sinx=-sin30=-1/2
Find out the value of tanθ
tanθ=tanx
[tex]tanθ=tanx=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}[/tex]
