Question

On a unit circle, the terminal point of 8 is ( 3 , 3 1). What is e?O A.radiansB.Eloradiansc. radiansOD. radians

Answer 1

We have a unit circle (radius = 1).

Then we can relate the x and y coordinates to the angle θ as:

$\begin{gathered} x=\cos (\theta) \\ y=\sin (\theta) \end{gathered}$

As the terminal point is (x,y)=((3^0.5)/2, 1/2), we can use any of these coordinates to find θ.

We will use y=1/2:

$\begin{gathered} y=\sin (\theta)=\frac{1}{2} \\ \theta=\arcsin (\frac{1}{2}) \\ \theta=\frac{\pi}{6} \end{gathered}$

Answer: the angle θ is θ = π/6

NOTE: we could have obtained the same result with x:

$\theta=\arccos (\sqrt[]{\frac{3}{2})}=\frac{\pi}{6}$