Test Objectives
  • Demonstrate the ability to solve trigonometric equations using square roots
  • Demonstrate the ability to solve trigonometric equations using square roots
  • Demonstrate the ability to solve trigonometric equations using square roots
Solving Trigonometric Equations Part III Practice Test:

#1:

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

$$a)\hspace{.1em}-\text{cos}^2 θ=3 - 5 \text{cos}^2 θ$$

$$b)\hspace{.1em}1 + 3\text{tan}^2 θ=4 \text{tan}^2 θ$$


#2:

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

$$a)\hspace{.1em}7=4\text{sin}^2 θ + 4$$

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


#3:

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

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

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


#4:

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

$$a)\hspace{.1em}\text{cot}^2 θ - 3\text{csc}\hspace{.1em}θ + 3=0$$

$$b)\hspace{.1em}3\text{sin}^2 θ + 2=\text{cos}^2 θ - 4 \text{sin}\hspace{.1em}θ$$


#5:

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

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

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


Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}\left\{\frac{π}{6}, \frac{5π}{6}, \frac{7π}{6}, \frac{11π}{6}\right\}$$

$$b)\hspace{.1em}\left\{\frac{π}{4}, \frac{3π}{4}, \frac{5π}{4}, \frac{7π}{4}\right\}$$


#2:

Solutions:

$$a)\hspace{.1em}\left\{\frac{π}{3}, \frac{2π}{3}, \frac{4π}{3}, \frac{5π}{3}\right\}$$

$$b)\hspace{.1em}\left\{\frac{π}{4}, \frac{3π}{4}, \frac{5π}{4}, \frac{7π}{4}\right\}$$


#3:

Solutions:

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

$$b)\hspace{.1em}\left\{\frac{π}{6}, \frac{π}{2}, \frac{5π}{6}\right\}$$


#4:

Solutions:

$$a)\hspace{.1em}\left\{\frac{π}{6}, \frac{π}{2}, \frac{5π}{6}\right\}$$

$$b)\hspace{.1em}\left\{\frac{7π}{6}, \frac{11π}{6}\right\}$$


#5:

Solutions:

$$a)\hspace{.1em}\{π\}$$

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