Question

find the terminal point $p(x, y)$ on the unit circle determined by the given value of $t$.
$t = -\frac{\pi}{2}$
$p(x, y) = ( )$
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Explanation:

Step1: Recall unit - circle formula

The coordinates of a terminal point $P(x,y)$ on the unit circle are given by $x = \cos t$ and $y=\sin t$.

Step2: Substitute $t =-\frac{\pi}{2}$ for $x$

$x=\cos(-\frac{\pi}{2})$. Since $\cos(-\alpha)=\cos\alpha$, then $x = 0$.

Step3: Substitute $t =-\frac{\pi}{2}$ for $y$

$y = \sin(-\frac{\pi}{2})$. Since $\sin(-\alpha)=-\sin\alpha$, then $y=- 1$.

Answer:

$(0,-1)$