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 $\theta =-\frac{\pi}{10}$, we have $\sin(-\frac{\pi}{10})=-\sin(\frac{\pi}{10})$. Since $\sin(\frac{\pi}{10}) = 0.3090$, then $\sin(-\frac{\pi}{10})=- 0.3090$.

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

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

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

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

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

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

Answer:

1. $-0.3090$; 23. $0.3090$; 24. $-0.3090$; 25. $-0.3090$