find the point (x,y) on the unit circle that corresponds to the real number t

Question

t=π/4

I tried to solve this problem but i dont even know where to start! i thought you had to divide the pie into 4 then put it on a number line, but when i checked my answer it was like in quadratic form can someone please help.

Answer 1

Hints:

The point $\;(x,y)\;$ is on the unit circle iff

$$\;x^2+y^2=1\;\iff \begin{cases}x=\cos t\\y=\sin t\end{cases}\;,\;\;t\in[0,2\pi)$$

So now just substitute $\;t=\frac\pi4\;$ to obtain your point (it has the same first and second entry, by the way)

Answer 2

Notice that an angle of $t=\pi/4$ in standard position has a terminal side that bisects the first quadrant. Thus, finding the desired point $(x,y)$ is equivalent to finding the point in the first quadrant where $y=x$ intersects $x^2+y^2=1$.