The forms R cos(theta ± a) and R sin(theta ± a) Quiz

1. What is $R$ if $5\cos\theta+12\sin\theta=R\cos(\theta-\alpha)$?

• A. $17$
• B. $13$
• C. $\sqrt{17}$
• D. $7$

2. What is the maximum value of $8\cos\theta+6\sin\theta$?

• A. $14$
• B. $100$
• C. $\sqrt{14}$
• D. $10$

3. What is the minimum value of $3\cos\theta+4\sin\theta$?

• A. $-7$
• B. $-1$
• C. $-5$
• D. $5$

4. How many solutions does $5\cos\theta+12\sin\theta=14$ have?

• A. none
• B. one
• C. two
• D. four

5. If $3\sin\theta+4\cos\theta=R\sin(\theta+\alpha)$, what is $\tan\alpha$?

• A. $\frac34$
• B. $\frac43$
• C. $\frac35$
• D. $\frac54$