Test Objectives
• Demonstrate the ability to find the trigonometric function values of an acute angle
• Demonstrate the ability to write a function in terms of its cofunction
• Demonstrate the ability to solve equations using cofunction identities
Trigonometric Functions of Acute Angles Practice Test:

#1:

Instructions: Find the six trigonometric functions for angle θ.

$$a)\hspace{.1em}$$

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

#2:

Instructions: Find the six trigonometric functions for angle θ.

$$a)\hspace{.1em}$$

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

#3:

Instructions: Write each function in terms of its cofunction.

$$a)\hspace{.1em}\text{cos}\hspace{.2em}51°$$

$$b)\hspace{.1em}\text{csc}\hspace{.2em}19°$$

#4:

Instructions: Write each function in terms of its cofunction.

$$a)\hspace{.1em}\text{cot}\hspace{.2em}77°$$

$$b)\hspace{.1em}\text{sec}(θ + 15°)$$

#5:

Instructions: Find one solution for each equation. Assume all angles are acute angles.

$$a)\hspace{.1em}\text{sin}(3θ - 6°)=\text{cos}(5θ-48°)$$

$$b) \hspace{.1em}\text{csc}(θ + 8°)=\text{sec}(3θ+10°)$$

Written Solutions:

#1:

Solutions:

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

$$b)\hspace{.1em}$$ $$\text{sin}\hspace{.2em}θ=\frac{7}{25}$$ $$\text{cos}\hspace{.2em}θ=\frac{24}{25}$$ $$\text{tan}\hspace{.2em}θ=\frac{7}{24}$$ $$\text{csc}\hspace{.2em}θ=\frac{25}{7}$$ $$\text{sec}\hspace{.2em}θ=\frac{25}{24}$$ $$\text{cot}\hspace{.2em}θ=\frac{24}{7}$$

#2:

Solutions:

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

$$b)\hspace{.1em}$$ $$\text{sin}\hspace{.2em}θ=\frac{2}{7}$$ $$\text{cos}\hspace{.2em}θ=\frac{3\sqrt{5}}{7}$$ $$\text{tan}\hspace{.2em}θ=\frac{2\sqrt{5}}{15}$$ $$\text{csc}\hspace{.2em}θ=\frac{7}{2}$$ $$\text{sec}\hspace{.2em}θ=\frac{7\sqrt{5}}{15}$$ $$\text{cot}\hspace{.2em}θ=\frac{3\sqrt{5}}{2}$$

#3:

Solutions:

$$a)\hspace{.1em}\text{cos}\hspace{.2em}51°=\text{sin}\hspace{.2em}39°$$

$$b)\hspace{.1em}\text{csc}\hspace{.2em}19°=\text{sec}\hspace{.2em}71°$$

#4:

Solutions:

$$a)\hspace{.1em}\text{cot}\hspace{.2em}77°=\text{tan}\hspace{.2em}13°$$

$$b)\hspace{.1em}\text{sec}(θ + 15°)=\text{csc}(75° - θ)$$

#5:

Solutions:

$$a)\hspace{.1em}θ=18°$$

$$b)\hspace{.1em}θ=18°$$