Question

for #22 - 25, use the given statement to complete the table.
given: $\sin\frac{\pi}{10}=.3090$

1. $-\frac{\pi}{10}$
2. $\frac{9\pi}{10}$
3. $\frac{11\pi}{10}$
4. $\frac{19\pi}{10}$

Explanation:

Step1: Use the property of sine function \(\sin(-x)=-\sin x\)

For \(\theta =-\frac{\pi}{10}\), \(\sin(-\frac{\pi}{10})=-\sin\frac{\pi}{10}\)
Since \(\sin\frac{\pi}{10} = 0.3090\), then \(\sin(-\frac{\pi}{10})=- 0.3090\)

Step2: Use the identity \(\sin(\pi - x)=\sin x\)

For \(\theta=\frac{9\pi}{10}=\pi-\frac{\pi}{10}\), \(\sin(\frac{9\pi}{10})=\sin(\pi - \frac{\pi}{10})=\sin\frac{\pi}{10}=0.3090\)

Step3: Use the identity \(\sin(\pi + x)=-\sin x\)

For \(\theta=\frac{11\pi}{10}=\pi+\frac{\pi}{10}\), \(\sin(\frac{11\pi}{10})=\sin(\pi+\frac{\pi}{10})=-\sin\frac{\pi}{10}=-0.3090\)

Step4: Use the identity \(\sin(2\pi - x)=-\sin x\)

For \(\theta=\frac{19\pi}{10}=2\pi-\frac{\pi}{10}\), \(\sin(\frac{19\pi}{10})=\sin(2\pi-\frac{\pi}{10})=-\sin\frac{\pi}{10}=-0.3090\)

Answer:

1. \(-0.3090\)
2. \(0.3090\)
3. \(-0.3090\)
4. \(-0.3090\)