Test Objectives
• Demonstrate the ability to solve problems using the Reciprocal Identities
• Demonstrate the ability to solve problems using the Pythagorean Identities
• Demonstrate the ability to solve problems using the Quotient Identities
Pythagorean & Quotient Identities Practice Test:

#1:

Instructions: Use identities to find the value of each expression.

a) Find cos θ and cot θ $$\text{csc}\hspace{.2em}θ=-5, \text{cos}\hspace{.2em}θ > 0$$

b) Find sin θ and cot θ $$\text{tan}\hspace{.2em}θ=-\frac{5}{6}, \text{csc}\hspace{.2em}θ > 0$$

#2:

Instructions: Use identities to find the value of each expression.

a) Find cos θ and tan θ $$\text{sec}\hspace{.2em}θ=-\frac{6}{5}, \text{cot}\hspace{.2em}θ < 0$$

b) Find sin θ and cos θ $$\text{cot}\hspace{.2em}θ=\frac{7}{5}, \text{sec}\hspace{.2em}θ > 0$$

#3:

Instructions: Use identities to find the value of each expression.

a) Find tan θ and cos θ $$\text{sin}\hspace{.2em}θ=\frac{1}{2}, \text{cot}\hspace{.2em}θ > 0$$

b) Find csc θ and sin θ $$\text{tan}\hspace{.2em}θ=\frac{1}{2}, \text{sec}\hspace{.2em}θ < 0$$

#4:

Instructions: Use identities to find the value of each expression.

a) Find sec θ and csc θ $$\text{sin}\hspace{.2em}θ=\frac{2}{3}, \text{cot}\hspace{.2em}θ > 0$$

b) Find cos θ and sin θ $$\text{csc}\hspace{.2em}θ=-\frac{5}{3}, \text{tan}\hspace{.2em}θ < 0$$

#5:

Instructions: Use identities to find the value of each expression.

a) Find sin θ and cos θ $$\text{sec}\hspace{.2em}θ=-\frac{7}{3}, \text{sin}\hspace{.2em}θ > 0$$

b) Find tan θ and cot θ $$\text{cos}\hspace{.2em}θ=-\frac{2}{5}, \text{csc}\hspace{.2em}θ > 0$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}\text{cos}\hspace{.2em}θ=\frac{2\sqrt{6}}{5}, \text{cot}\hspace{.2em}θ=-2\sqrt{6}$$

$$b)\hspace{.1em}\text{sin}\hspace{.2em}θ=\frac{5\sqrt{61}}{61}, \text{cot}\hspace{.2em}θ=-\frac{6}{5}$$

#2:

Solutions:

$$a)\hspace{.1em}\text{cos}\hspace{.2em}θ=-\frac{5}{6}, \text{tan}\hspace{.2em}θ=-\frac{\sqrt{11}}{5}$$

$$b)\hspace{.1em}\text{sin}\hspace{.2em}θ=\frac{5\sqrt{74}}{74}, \text{cos}\hspace{.2em}θ=\frac{7\sqrt{74}}{74}$$

#3:

Solutions:

$$a)\hspace{.1em}\text{tan}\hspace{.2em}θ=\frac{\sqrt{3}}{3}, \text{cos}\hspace{.2em}θ=\frac{\sqrt{3}}{2}$$

$$b)\hspace{.1em}\text{csc}\hspace{.2em}θ=-\sqrt{5}, \text{sin}\hspace{.2em}θ=-\frac{\sqrt{5}}{5}$$

#4:

Solutions:

$$a)\hspace{.1em}\text{sec}\hspace{.2em}θ=\frac{3\sqrt{5}}{5}, \text{csc}\hspace{.2em}θ=\frac{3}{2}$$

$$b)\hspace{.1em}\text{cos}\hspace{.2em}θ=\frac{4}{5}, \text{sin}\hspace{.2em}θ=-\frac{3}{5}$$

#5:

Solutions:

$$a)\hspace{.1em}\text{sin}\hspace{.2em}θ=\frac{2\sqrt{10}}{7}, \text{cos}\hspace{.2em}θ=-\frac{3}{7}$$

$$b)\hspace{.1em}\text{tan}\hspace{.2em}θ=-\frac{\sqrt{21}}{2}, \text{cot}\hspace{.2em}θ=-\frac{2\sqrt{21}}{21}$$