Question

you can drag the terminal point in the given applet to rotate the angles terminal ray. as you drag the point, the angles measurement θ (in radians) is shown.
θ = 0.01
by using the applet above, fill in the table of values below.
now, sketch a graph of v = sin(θ) based on the information in the table above.

Explanation:

Step1: Recall the sine function values

We know that for the sine function \(y = \sin(\theta)\), when \(\theta=0\), \(\sin(0) = 0\); when \(\theta=\frac{\pi}{2}\), \(\sin(\frac{\pi}{2}) = 1\); when \(\theta=\pi\), \(\sin(\pi)=0\); when \(\theta=\frac{3\pi}{2}\), \(\sin(\frac{3\pi}{2})=- 1\); when \(\theta = 2\pi\), \(\sin(2\pi)=0\).

Step2: Fill in the table

For \(\theta = 0\), \(\sin(0)=0\); for \(\theta=\frac{\pi}{2}\), \(\sin(\frac{\pi}{2}) = 1\); for \(\theta=\pi\), \(\sin(\pi)=0\); for \(\theta=\frac{3\pi}{2}\), \(\sin(\frac{3\pi}{2})=-1\); for \(\theta = 2\pi\), \(\sin(2\pi)=0\).

Answer:

\(2\pi\)	\(\frac{3\pi}{2}\)	\(\pi\)	\(\frac{\pi}{2}\)	\(0\)	\(\theta\)