Test Objectives
• Demonstrate the ability to find function values of an angle
Trigonometric Functions Practice Test:

#1:

Instructions: Use the given point on the terminal side of angle θ to find the value of the trigonometric function indicated.

$$a)\hspace{.1em}\text{sin}\hspace{.25em}θ, \hspace{.25em}\left(\sqrt{5}, 2\right)$$

$$b)\hspace{.1em}\text{csc}\hspace{.25em}θ, \hspace{.25em}\left(2, 2\sqrt{3}\right)$$

#2:

Instructions: Use the given point on the terminal side of angle θ to find the value of the trigonometric function indicated.

$$a)\hspace{.1em}\text{sec}\hspace{.25em}θ, \hspace{.25em}\left(3, -\sqrt{7}\right)$$

$$b)\hspace{.1em}\text{cot}\hspace{.25em}θ, \hspace{.25em}\left(-\sqrt{15}, -7\right)$$

#3:

Instructions: Use the given point on the terminal side of angle θ to find the value of the trigonometric function indicated.

$$a)\hspace{.1em}\text{cos}\hspace{.25em}θ, \hspace{.25em}\left(-6, -\sqrt{13}\right)$$

$$b)\hspace{.1em}\text{sec}\hspace{.25em}θ, \hspace{.25em}\left(-2\sqrt{5}, -4\right)$$

#4:

Instructions: Use the given point on the terminal side of angle θ to find the value of the trigonometric function indicated.

$$a)\hspace{.1em}\text{sec}\hspace{.25em}θ, \hspace{.25em}\left(2\sqrt{3}, -2\right)$$

$$b)\hspace{.1em}\text{cos}\hspace{.25em}θ, \hspace{.25em}\left({-}\sqrt{13}, 6\right)$$

#5:

Instructions: Find the trigonometric function values of angle θ if its terminal side is defined by the given ray.

$$a)\hspace{.1em}{-}6x - y=0, x ≤ 0$$

$$b) \hspace{.1em}{-}4x + 7y=0, x ≤ 0$$

Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}\text{sin}\hspace{.25em}θ=\frac{2}{3}$$

$$b)\hspace{.1em}\text{csc}\hspace{.25em}θ=\frac{2\sqrt{3}}{3}$$

#2:

Solutions:

$$a)\hspace{.1em}\text{sec}\hspace{.25em}θ=\frac{4}{3}$$

$$b)\hspace{.1em}\text{cot}\hspace{.25em}θ=\frac{\sqrt{15}}{7}$$

#3:

Solutions:

$$a)\hspace{.1em}\text{cos}\hspace{.25em}θ={-}\frac{6}{7}$$

$$b)\hspace{.1em}\text{sec}\hspace{.25em}θ={-}\frac{3\sqrt{5}}{5}$$

#4:

Solutions:

$$a)\hspace{.1em}\text{sec}\hspace{.25em}θ=\frac{2\sqrt{3}}{3}$$

$$b)\hspace{.1em}\text{cos}\hspace{.25em}θ={-}\frac{\sqrt{13}}{7}$$

#5:

Solutions:

$$a)\hspace{.1em}\text{sin}\hspace{.25em}θ=\frac{6\sqrt{37}}{37}$$ $$\text{cos}\hspace{.25em}θ=-\frac{\sqrt{37}}{37}$$ $$\text{tan}\hspace{.25em}θ=-6$$ $$\text{csc}\hspace{.25em}θ=\frac{\sqrt{37}}{6}$$ $$\text{sec}\hspace{.25em}θ=-\sqrt{37}$$ $$\text{cot}\hspace{.25em}θ=-\frac{1}{6}$$

$$b)\hspace{.1em}\text{sin}\hspace{.25em}θ=-\frac{4\sqrt{65}}{65}$$ $$\text{cos}\hspace{.25em}θ=-\frac{7\sqrt{65}}{65}$$ $$\text{tan}\hspace{.25em}θ=\frac{4}{7}$$ $$\text{csc}\hspace{.25em}θ=-\frac{\sqrt{65}}{4}$$ $$\text{sec}\hspace{.25em}θ=-\frac{\sqrt{65}}{7}$$ $$\text{cot}\hspace{.25em}θ=\frac{7}{4}$$