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.

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

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


#2:

Instructions: Find the exact value.

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

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


#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.

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

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


#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:

$$a)\hspace{.1em}-\frac{π}{3}$$

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


#2:

Solutions:

$$a)\hspace{.1em}\frac{2π}{3}$$

$$b)\hspace{.1em}\frac{3π}{4}$$


#3:

Solutions:

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

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


#4:

Solutions:

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

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


#5:

Solutions:

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

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