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.

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

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


#2:

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

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

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


#3:

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

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

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


#4:

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

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

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


#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:

$$a)\hspace{.1em}\frac{2}{3}$$

$$b)\hspace{.1em}\frac{2\sqrt{3}}{3}$$


#2:

Solutions:

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

$$b)\hspace{.1em}\frac{\sqrt{15}}{7}$$


#3:

Solutions:

$$a)\hspace{.1em}-\frac{6}{7}$$

$$b)\hspace{.1em}-\frac{3\sqrt{5}}{5}$$


#4:

Solutions:

$$a)\hspace{.1em}\frac{2\sqrt{3}}{3}$$

$$b)\hspace{.1em}-\frac{\sqrt{13}}{7}$$


#5:

Solutions:

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

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