Solving trigonometric equations Quiz

1. Solve $\sin x=0.5$ for $0\le x\le360^\circ$.

• A. $30^\circ$, $330^\circ$
• B. $30^\circ$, $150^\circ$
• C. $60^\circ$, $120^\circ$
• D. $150^\circ$, $210^\circ$

2. Solve $\tan x=-1$ for $0\le x<360^\circ$.

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

3. For $\cos3x=0.5$ with $0\le x<360^\circ$, the interval for $3x$ is...

• A. $0\le3x<120^\circ$
• B. $0\le3x<360^\circ$
• C. $0\le3x<1080^\circ$
• D. $0\le3x<720^\circ$

4. Which are the possible values of $\cos x$ if $2\cos^2x-\cos x-1=0$?

• A. $1$ and $\frac12$
• B. $-1$ and $\frac12$
• C. $-1$ and $-\frac12$
• D. $1$ and $-\frac12$

5. How many solutions does $\cos3x=0.5$ have for $0\le x<360^\circ$?

• A. $3$
• B. $2$
• C. $6$
• D. $9$