Question

(a) if we mark off a distance t along the unit circle, starting at (1, 0) and moving in a counterclockwise direction, we arrive at the ---select--- point determined by t.
(b) what are the terminal points determined by π/2, π, -π/2, and 2π?
π/2 (x, y) = (
π (x, y) = (
-π/2 (x, y) = (
2π (x, y) = (
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Explanation:

Step1: Recall unit - circle properties

On the unit circle $x = \cos t$ and $y=\sin t$, where $t$ is the angle measured counter - clockwise from the positive $x$ - axis.

Step2: Find terminal point for $t=\frac{\pi}{2}$

When $t = \frac{\pi}{2}$, $x=\cos(\frac{\pi}{2}) = 0$ and $y=\sin(\frac{\pi}{2})=1$. So the terminal point is $(0,1)$.

Step3: Find terminal point for $t = \pi$

When $t=\pi$, $x=\cos(\pi)=- 1$ and $y=\sin(\pi)=0$. So the terminal point is $(-1,0)$.

Step4: Find terminal point for $t=-\frac{\pi}{2}$

When $t =-\frac{\pi}{2}$, $x=\cos(-\frac{\pi}{2}) = 0$ and $y=\sin(-\frac{\pi}{2})=-1$. So the terminal point is $(0, - 1)$.

Step5: Find terminal point for $t = 2\pi$

When $t = 2\pi$, $x=\cos(2\pi)=1$ and $y=\sin(2\pi)=0$. So the terminal point is $(1,0)$.

Answer:

$\frac{\pi}{2}:(0,1)$
$\pi:(-1,0)$
$-\frac{\pi}{2}:(0, - 1)$
$2\pi:(1,0)$