Test Objectives
  • Demonstrate the ability to solve basic trigonometric equations
  • Demonstrate the ability to solve trigonometric equations with half-angles
Solving Trigonometric Equations Part IV Practice Test:

#1:

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

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

$$b)\hspace{.1em}0=\text{cos}\hspace{.1em}\frac{θ}{2}+ \text{sin}\hspace{.1em}θ$$


#2:

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

$$a)\hspace{.1em}-1 + \text{sin}\hspace{.1em}\frac{θ}{2}+ \text{cos}\hspace{.1em}θ=0$$

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


#3:

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

$$a)\hspace{.1em}\sqrt{3}\text{cos}\hspace{.1em}\frac{θ}{2}+ \text{cos}\hspace{.1em}θ + 1=0$$

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


#4:

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

$$a)\hspace{.1em}-\text{cos}\hspace{.1em}θ + \sqrt{3}\text{sin}\hspace{.1em}\frac{θ}{2}=-1$$

$$b)\hspace{.1em}0=\text{cos}\hspace{.1em}θ + \text{cos}\hspace{.1em}\frac{θ}{2}$$


#5:

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

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

$$b)\hspace{.1em}-2 - \text{cos}\hspace{.1em}θ + 3 \text{cos}\hspace{.1em}\frac{θ}{2}=0$$


Written Solutions:

#1:

Solutions:

$$a)\hspace{.1em}\left\{0\right\}$$

$$b)\hspace{.1em}\left\{π\right\}$$


#2:

Solutions:

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

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


#3:

Solutions:

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

$$b)\hspace{.1em}\left\{0, π\right\}$$


#4:

Solutions:

$$a)\hspace{.1em}\left\{0\right\}$$

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


#5:

Solutions:

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

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