Question

Find the terminal point on the unit circle determined by π3 radians.Use exact values, not decimal approximations.

Answer 1

Using a graph of the unitary circle,

Every point on the unitary circle can be expressed as (cosθ,sinθ).

In our case, since θ=pi/3,

$\begin{gathered} \theta=\frac{\pi}{3} \\ \Rightarrow(x,y)=(\cos(\frac{\pi}{3}),\sin(\frac{\pi}{3})) \end{gathered}$

Then,

$\Rightarrow(x,y)=(\frac{1}{2},\frac{\sqrt{3}}{2})$

Thus, the answer is (1/2,sqrt(3)/2)