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=(\pi)/(3) \\ \Rightarrow(x,y)=(\cos((\pi)/(3)),\sin((\pi)/(3))) \end{gathered}`

Then,

`\Rightarrow(x,y)=((1)/(2),(√(3))/(2))`

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