Answer
$y=\sin{0} = 0$, thus, the point is $(0, 0)$
$y=\sin{\frac{\pi}{4}} = \frac{\sqrt2}{2}$, thus, the point is $(\frac{\pi}{4}, \frac{\sqrt2}{2})$
$y=\sin{\frac{\pi}{2}} = 1$, thus, the point is $(\frac{\pi}{2}, 1)$
$y=\sin{\frac{3\pi}{4}} = \frac{\sqrt2}{2}$, thus, the point is $(\frac{3\pi}{4}, \frac{\sqrt2}{2})$
$y=\sin{\pi} = 0$, thus, the point is $(\pi, 0)$
Work Step by Step
All the given values of $x$ are either special angles or have a special angle as their reference angle. Hence, the value of the sine for each angle can be easily found.
Evaluate the function for each given value of $x$ to obtain:
When $x=0$:
$y=\sin{0} = 0$, thus, the point is $(0, 0)$
When $x=\frac{\pi}{4}$:
$y=\sin{\frac{\pi}{4}} = \frac{\sqrt2}{2}$, thus, the point is $(\frac{\pi}{4}, \frac{\sqrt2}{2})$
When $x=\frac{\pi}{2}$:
$y=\sin{\frac{\pi}{2}} = 1$, thus, the point is $(\frac{\pi}{2}, 1)$
When $x=\frac{3\pi}{4}$:
Reference angle is $\frac{\pi}{4}$. Since the angle is in Quadrant II, sine is positive. Thus,
$y=\sin{\frac{3\pi}{4}} = \sin{\frac{\pi}{4}}=\frac{\sqrt2}{2}$
Thus, the point is $(\frac{3\pi}{4}, \frac{\sqrt2}{2})$
When $x=\pi$:
$y=\sin{\pi} = 0$, thus, the point is $(\pi, 0)$
