Answer
$y=2\sin{0} = 2(0)=0$, thus, the point is $(0, 0)$
$y=2\sin{\frac{\pi}{2}} = 2(1)=2$, thus, the point is $(\frac{\pi}{2}, 2)$
$y=2\sin{\pi} = 2(0)=0$, thus, the point is $(\pi, 0)$
$y=2\sin{\frac{3\pi}{2}} = 2(-\sin{\frac{\pi}{2}})=2(-1)=-2$, thus, the point is $(\frac{3\pi}{2}, -2)$
$y=2\sin{2\pi} =2(0)=0$, thus, the point is $(2\pi, 0)$
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 cosine for each angle can be easily found.
Evaluate the function for each given value of $x$ to obtain:
When $x=0$:
$y=2\sin{0} = 2(0)=0$, thus, the point is $(0, 0)$
When $x=\frac{\pi}{2}$:
$y=2\sin{\frac{\pi}{2}} = 2(1)=2$, thus, the point is $(\frac{\pi}{2}, 2)$
When $x=\pi$:
$y=2\sin{\pi} = 2(0)=0$, thus, the point is $(\pi, 0)$
When $x=\frac{3\pi}{2}$:
Reference angle is $\frac{\pi}{2}$. Since the angle is on the negative y-axis, then sine is negative. Thus,
$y=2\sin{\frac{3\pi}{2}} = 2(-\sin{\frac{\pi}{2}})=2(-1)=-2$
Thus, the point is $(\frac{3\pi}{2}, -2)$.
When $x=2\pi$:
$y=2\sin{2\pi} =2(0)=0$, thus, the point is $(2\pi, 0)$
