Test Objectives
  • Demonstrate the ability to solve basic trigonometric equations
  • Demonstrate the ability to solve trigonometric equations using factoring
Solving Trigonometric Equations Part II Practice Test:

#1:

Instructions: Solve each equation for 0 ≤ θ < 2π.

$$a)\hspace{.1em}-4\text{sec}\hspace{.1em}θ + 4 + 2\text{sec}^2 θ=\text{sec}^2 θ$$

$$b)\hspace{.1em}-2\text{cot}\hspace{.1em}θ=\sqrt{3}\text{tan}\hspace{.1em}θ \text{cot}\hspace{.1em}θ + \text{tan}\hspace{.1em}θ - 2\text{cot}\hspace{.1em}θ$$


#2:

Instructions: Solve each equation for 0 ≤ θ < 2π.

$$a)\hspace{.1em}3\text{cos}\hspace{.1em}θ=1 + 2\text{cos}^2 θ$$

$$b)\hspace{.1em}1 + 3\text{cos}^2 θ + 3 \text{cos}\hspace{.1em}θ=\text{cos}^2 θ$$


#3:

Instructions: Solve each equation for 0 ≤ θ < 2π.

$$a)\hspace{.1em}3\text{csc}\hspace{.1em}θ=\sqrt{3}\text{csc}\hspace{.1em}θ \text{tan}\hspace{.1em}θ + 2 \text{csc}\hspace{.1em}θ$$

$$b)\hspace{.1em}-\sqrt{3}\text{sec}\hspace{.1em}θ \text{tan}\hspace{.1em}θ + 4\text{sec}\hspace{.1em}θ=3\text{sec}\hspace{.1em}θ$$


#4:

Instructions: Solve each equation for 0 ≤ θ < 2π.

$$a)\hspace{.1em}-1 - 2\text{cot}^2 θ=-\text{cot}^2 θ + 2 \text{cot}\hspace{.1em}θ$$

$$b)\hspace{.1em}-\sqrt{3}\text{cot}\hspace{.1em}θ + 2 \text{cot}\hspace{.1em}θ\text{sin}\hspace{.1em}θ - 3\text{sin}\hspace{.1em}θ=-3\text{sin}\hspace{.1em}θ$$


#5:

Instructions: Solve each equation for 0 ≤ θ < 2π.

$$a)\hspace{.1em}-2=-\text{sec}^2 θ - \text{sec}\hspace{.1em}θ$$

$$b)\hspace{.1em}\sqrt{3}\text{sec}\hspace{.1em}θ + 3 \text{sec}\hspace{.1em}θ \text{cot}\hspace{.1em}θ=0$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}\left\{\frac{π}{3}, \frac{5π}{3}\right\}$$

$$b)\hspace{.1em}\left\{\frac{2π}{3}, \frac{5π}{3}\right\}$$


#2:

Solutions:

$$a)\hspace{.1em}\left\{0, \frac{π}{3}, \frac{5π}{3}\right\}$$

$$b)\hspace{.1em}\left\{\frac{2π}{3}, π, \frac{4π}{3}\right\}$$


#3:

Solutions:

$$a)\hspace{.1em}\left\{\frac{π}{6}, \frac{7π}{6}\right\}$$

$$b)\hspace{.1em}\left\{\frac{π}{6}, \frac{7π}{6}\right\}$$


#4:

Solutions:

$$a)\hspace{.1em}\left\{\frac{3π}{4}, \frac{7π}{4}\right\}$$

$$b)\hspace{.1em}\left\{\frac{π}{3}, \frac{π}{2}, \frac{2π}{3}, \frac{3π}{2}\right\}$$


#5:

Solutions:

$$a)\hspace{.1em}\left\{0, \frac{2π}{3}, \frac{4π}{3}\right\}$$

$$b)\hspace{.1em}\left\{\frac{2π}{3}, \frac{5π}{3}\right\}$$