Given the terminal point of Θ:
[tex](\frac{1}{2},\frac{\sqrt[]{3}}{2})[/tex]
Let's find the value of Θ.
In polar coordinates, we have the points as
[tex]P=(R,\theta)[/tex]
Where:
R is the radius and Θ is the angle.
We know in rectangular coordinates, we have:
x = R * cosΘ
Y = R * sinΘ
Thus, to find the value of Θ, we have:
[tex]\sin \theta=\frac{\sqrt[]{3}}{2}[/tex]
Solve for Θ.
[tex]\begin{gathered} \\ \text{sin}\theta=\frac{\sqrt[]{3}}{2} \\ \end{gathered}[/tex]
Take the inverse cosine of both sides:
[tex]\begin{gathered} \theta=\sin ^{-1}(\frac{\sqrt[]{3}}{2}) \\ \\ \theta=\frac{\pi}{3} \end{gathered}[/tex]
ANSWER:
[tex]C.\text{ }\frac{\pi}{3}radians[/tex]
