Test Objectives
• Demonstrate the ability to evaluate an inverse sine function
• Demonstrate the ability to evaluate an inverse cosine function
• Demonstrate the ability to evaluate an inverse tangent function
• Demonstrate the ability to evaluate an inverse secant function
• Demonstrate the ability to evaluate an inverse cosecant function
• Demonstrate the ability to evaluate an inverse cotangent function
Inverse Trigonometric Functions Practice Test:

#1:

Instructions: Find the exact value.

$$a)\hspace{.1em}\text{sin}^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$

$$b)\hspace{.1em}\text{tan}^{-1}\left(0\right)$$

$$c)\hspace{.1em}\text{sec}^{-1}\left(-2\right)$$

$$d)\hspace{.1em}\text{cot}^{-1}\left(-1\right)$$

$$e)\hspace{.1em}\text{cot}^{-1}\left(\sqrt{3}\right)$$

$$f)\hspace{.1em}\text{csc}^{-1}\left(-\sqrt{2}\right)$$

#2:

Instructions: Find the exact value.

$$a)\hspace{.1em}\text{sin}^{-1}\left(\text{sin}\frac{3π}{4}\right)$$

$$b)\hspace{.1em}\text{cos}^{-1}\left(\text{cos}\frac{2π}{3}\right)$$

$$c)\hspace{.1em}\text{tan}^{-1}\left(\text{tan}\frac{11π}{6}\right)$$

#3:

Instructions: Find the exact value.

$$a)\hspace{.1em}\text{csc}\left(\text{sin}^{-1}\left(\frac{12}{13}\right)\right)$$

$$b)\hspace{.1em}\text{tan}\left(\text{cos}^{-1}\left(\frac{3}{5}\right)\right)$$

#4:

Instructions: Find the exact value.

$$a)\hspace{.1em}\text{cot}\left(\text{sin}^{-1}\left(\frac{3}{4}\right)\right)$$

Instructions: Write as an algebraic expression in u.

$$b)\hspace{.1em}\text{sec}\left(\text{sin}^{-1}\left(\frac{u}{\sqrt{u^2 + 4}}\right)\right)$$

#5:

Instructions: Find the exact value.

$$a)\hspace{.1em}\text{cos}\left(\text{tan}^{-1}\left(\frac{5}{12}\right) - \text{tan}^{-1}\left(\frac{3}{4}\right)\right)$$

$$b)\hspace{.1em}\text{tan}\left(2\text{sin}^{-1}\left(\frac{2}{5}\right)\right)$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}{-}\frac{π}{3}$$

$$b)\hspace{.1em}0$$

$$c)\hspace{.1em}\frac{2π}{3}$$

$$d)\hspace{.1em}\frac{3π}{4}$$

$$e)\hspace{.1em}\frac{π}{6}$$

$$f)\hspace{.1em}{-}\frac{π}{4}$$

#2:

Solutions:

$$a)\hspace{.1em}\frac{π}{4}$$

$$b)\hspace{.1em}\frac{2π}{3}$$

$$c)\hspace{.1em}{-}\frac{π}{6}$$

#3:

Solutions:

$$a)\hspace{.1em}\frac{13}{12}$$

$$b)\hspace{.1em}\frac{4}{3}$$

#4:

Solutions:

$$a)\hspace{.1em}\frac{\sqrt{7}}{3}$$

$$b)\hspace{.1em}\frac{\sqrt{u^2 + 4}}{2}$$ $$-\frac{π}{2}< θ < \frac{π}{2}$$

#5:

Solutions:

$$a)\hspace{.1em}\frac{63}{65}$$

$$b)\hspace{.1em}\frac{4 \sqrt{21}}{17}$$