Reciprocal and inverse trigonometric functions Quiz

1. $\cos\theta=\frac{5}{13}$ with $\theta$ acute. Find $\operatorname{cosec}\theta$.

• A. $\frac{13}{12}$
• B. $\frac{13}{5}$
• C. $\frac{12}{5}$
• D. $\frac{5}{12}$

2. Which statement is true for $y=\sec x$?

• A. Range is all real numbers
• B. Range is $-1\le y\le1$
• C. Range is $y\le-1$ or $y\ge1$
• D. Range is $y>0$

3. Simplify $\tan^2\theta+1$.

• A. $\operatorname{cosec}^2\theta$
• B. $\cot^2\theta$
• C. $\sin^2\theta$
• D. $\sec^2\theta$

4. Find $\arcsin\left(\frac{\sqrt3}{2}\right)$.

• A. $\frac{\pi}{3}$
• B. $\frac{\pi}{6}$
• C. $\frac{2\pi}{3}$
• D. $\frac{\pi}{4}$

5. Find $\arccos\left(\cos\frac{7\pi}{6}\right)$.

• A. $\frac{7\pi}{6}$
• B. $-\frac{\pi}{6}$
• C. $\frac{\pi}{6}$
• D. $\frac{5\pi}{6}$