Solving trigonometric equations Quiz

1. Solve $\tan x=1$ for $0^\circ\le x\le360^\circ$.

• A. $45^\circ$ and $135^\circ$
• B. $45^\circ$ and $225^\circ$
• C. $45^\circ$ and $315^\circ$
• D. $135^\circ$ and $315^\circ$

2. How many solutions does $\sin x=0.4$ have for $0^\circ\le x<720^\circ$?

• A. $2$
• B. $3$
• C. $4$
• D. $8$

3. Solve $\sin x=-\frac12$ for $0\le x<2\pi$.

• A. $\frac\pi6$ and $\frac{5\pi}6$
• B. $\frac{5\pi}6$ and $\frac{7\pi}6$
• C. $\frac{2\pi}3$ and $\frac{4\pi}3$
• D. $\frac{7\pi}6$ and $\frac{11\pi}6$

4. Solve $\cos(x-20^\circ)=0.5$ for $0^\circ\le x<360^\circ$.

• A. $80^\circ$ and $320^\circ$
• B. $40^\circ$ and $340^\circ$
• C. $60^\circ$ and $300^\circ$
• D. $80^\circ$ and $280^\circ$

5. How many solutions does $\tan3x=1$ have for $0^\circ\le x<180^\circ$?

• A. $2$
• B. $3$
• C. $4$
• D. $6$