Test Objectives
• Demonstrate the ability to find trigonometric function values given on value and the quadrant
Reciprocal Identities Practice Test:

#1:

Instructions: Find the values of the five trigonometric functions not given.

$$a)\hspace{.1em}\text{tan}\hspace{.2em}θ=\frac{2}{3}, \text{sin}\hspace{.2em}θ < 0$$

$$b)\hspace{.1em}\text{sec}\hspace{.2em}θ=-\frac{\sqrt{5}}{2}, \text{sin}\hspace{.2em}θ > 0$$

#2:

Instructions: Find the values of the five trigonometric functions not given.

$$a)\hspace{.1em}\text{tan}\hspace{.2em}θ=-\frac{2\sqrt{5}}{5}, \text{sin}\hspace{.2em}θ < 0$$

$$b)\hspace{.1em}\text{csc}\hspace{.2em}θ=\frac{\sqrt{17}}{4}, \text{cos}\hspace{.2em}θ > 0$$

#3:

Instructions: Find the values of the five trigonometric functions not given.

$$a)\hspace{.1em}\text{cot}\hspace{.2em}θ=-\frac{4}{3}, \text{cos}\hspace{.2em}θ < 0$$

$$b)\hspace{.1em}\text{tan}\hspace{.2em}θ=-\frac{2}{3}, \text{cos}\hspace{.2em}θ > 0$$

#4:

Instructions: Find the values of the five trigonometric functions not given.

$$a)\hspace{.1em}\text{sec}\hspace{.2em}θ=\frac{5}{4}, \text{sin}\hspace{.2em}θ < 0$$

$$b)\hspace{.1em}\text{sec}\hspace{.2em}θ=\frac{5}{4}, \text{sin}\hspace{.2em}θ > 0$$

#5:

Instructions: Find the values of the five trigonometric functions not given.

$$a)\hspace{.1em}\text{csc}\hspace{.2em}θ=-\frac{13}{12}, \text{cos}\hspace{.2em}θ > 0$$

$$b) \hspace{.1em}\text{sec}\hspace{.2em}θ=\frac{17}{15}, \text{sin}\hspace{.2em}θ < 0$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}\text{sin}\hspace{.2em}θ=-\frac{2\sqrt{13}}{13}$$ $$\text{cos}\hspace{.2em}θ=-\frac{3\sqrt{13}}{13}$$ $$\text{csc}\hspace{.2em}θ=-\frac{\sqrt{13}}{2}$$ $$\text{sec}\hspace{.2em}θ=-\frac{\sqrt{13}}{3}$$ $$\text{cot}\hspace{.2em}θ=\frac{3}{2}$$

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

#2:

Solutions:

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

$$b)\hspace{.1em}\text{sin}\hspace{.2em}θ=\frac{4\sqrt{17}}{17}$$ $$\text{cos}\hspace{.2em}θ=\frac{\sqrt{17}}{17}$$ $$\text{tan}\hspace{.2em}θ=4$$ $$\text{sec}\hspace{.2em}θ=\sqrt{17}$$ $$\text{cot}\hspace{.2em}θ=\frac{1}{4}$$

#3:

Solutions:

$$a)\hspace{.1em}\text{sin}\hspace{.2em}θ=\frac{3}{5}$$ $$\text{cos}\hspace{.2em}θ=-\frac{4}{5}$$ $$\text{tan}\hspace{.2em}θ=-\frac{3}{4}$$ $$\text{csc}\hspace{.2em}θ=\frac{5}{3}$$ $$\text{sec}\hspace{.2em}θ=-\frac{5}{4}$$

$$b)\hspace{.1em}\text{sin}\hspace{.2em}θ=-\frac{2\sqrt{13}}{13}$$ $$\text{cos}\hspace{.2em}θ=\frac{3\sqrt{13}}{13}$$ $$\text{csc}\hspace{.2em}θ=-\frac{\sqrt{13}}{2}$$ $$\text{sec}\hspace{.2em}θ=\frac{\sqrt{13}}{3}$$ $$\text{cot}\hspace{.2em}θ=-\frac{3}{2}$$

#4:

Solutions:

$$a)\hspace{.1em}\text{sin}\hspace{.2em}θ=-\frac{3}{5}$$ $$\text{cos}\hspace{.2em}θ=\frac{4}{5}$$ $$\text{tan}\hspace{.2em}θ=-\frac{3}{4}$$ $$\text{csc}\hspace{.2em}θ=-\frac{5}{3}$$ $$\text{cot}\hspace{.2em}θ=-\frac{4}{3}$$

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

#5:

Solutions:

$$a)\hspace{.1em}\text{sin}\hspace{.2em}θ=-\frac{12}{13}$$ $$\text{cos}\hspace{.2em}θ=\frac{5}{13}$$ $$\text{tan}\hspace{.2em}θ=-\frac{12}{5}$$ $$\text{sec}\hspace{.2em}θ=\frac{13}{5}$$ $$\text{cot}\hspace{.2em}θ=-\frac{5}{12}$$

$$b)\hspace{.1em}\text{sin}\hspace{.2em}θ=-\frac{8}{17}$$ $$\text{cos}\hspace{.2em}θ=\frac{15}{17}$$ $$\text{tan}\hspace{.2em}θ=-\frac{8}{15}$$ $$\text{csc}\hspace{.2em}θ=-\frac{17}{8}$$ $$\text{cot}\hspace{.2em}θ=-\frac{15}{8}$$