5.3 Solving Trigonometric Equations

Solving Trigonometric

equations

Referenced from the textbook, chapter 5.3

Multiple Select

Which angles make this equation true?

$$\sin\theta=\frac{1}{2}$$  

• $$\theta=\frac{\pi}{3}$$  

• $$\theta=\frac{\pi}{6}$$  

• $$\theta=\frac{7\pi}{6}$$  

• $$\theta=\frac{5\pi}{6}$$  

• $$\theta=\frac{\pi}{4}$$

Multiple Select

Which angles make this equation true?

$$\cos\theta=-\frac{\sqrt{2}}{2}$$  

• $$\frac{\pi}{4}$$  

• $$\frac{3\pi}{4}$$  

• $$\frac{5\pi}{4}$$  

• $$\frac{7\pi}{4}$$  

• $$\frac{\pi}{3}$$

Multiple Select

Select all angles that solves the following: $$\tan\theta=\sqrt{3}$$  

• $$\frac{\pi}{3}$$  

• $$\frac{2\pi}{3}$$  

• $$\frac{4\pi}{3}$$  

• $$\frac{5\pi}{3}$$  

Multiple Choice

Which angles make this equation true?

sinθ = -1 on θ∈[0, 2π)

• θ = π /2, 3π /2 

• θ = π /2

• θ = 3π /2

• θ = π  

When Solving Trig Equations

Main Strategies (will vary depending on the equation)

Isolate the trig function.
Change into sines and cosines

Combine like terms if necessary.

Factor if necessary.

Use your unit circle to determine the solutions.

Multiple Select

Solve for x (select all possible solutions)

$$2\cos x-1=0$$

• $$x=\frac{5\pi}{3}$$

• $$x=\frac{\pi}{3}$$

• $$x=\frac{\pi}{6}$$

• $$x=\frac{2\pi}{3}$$

• $$x=\frac{4\pi}{3}$$

Multiple Select

Solve for x (select all possible solutions)

$$\sec x+2=0$$

• $$x=\frac{5\pi}{3}$$

• $$x=\frac{\pi}{3}$$

• $$x=\frac{\pi}{6}$$

• $$x=\frac{2\pi}{3}$$

• $$x=\frac{4\pi}{3}$$

Multiple Select

Solve for x (select all possible solutions)

$$\sec x-4=-\sec x$$

• $$x=\frac{5\pi}{3}$$

• $$x=\frac{\pi}{3}$$

• $$x=\frac{\pi}{6}$$

• $$x=\frac{2\pi}{3}$$

• $$x=\frac{4\pi}{3}$$

Multiple Select

Find all possible solutions of the equation

$$4\sin^2x-3=0$$

• $$\theta=\frac{\pi}{3}$$

• $$\theta=\frac{2\pi}{3}$$

• $$\theta=\frac{4\pi}{3}$$

• $$\theta=\frac{5\pi}{3}$$

• $$\theta=\frac{5\pi}{6}$$

Multiple Select

Solve for x (select all possible solutions)

$$2\sin^2x+3\sin x+1=0$$

• $$x=\frac{3\pi}{2}$$

• $$x=\frac{7\pi}{6}$$

• $$x=\frac{11\pi}{6}$$

• $$x=\frac{2\pi}{3}$$

• $$x=\frac{4\pi}{3}$$

Multiple Select

Solve for x (select all possible solutions)

$$\sin^2x+\cos x+1=0$$

• $$x=\pi$$

• $$x=0$$

• $$x=\frac{\pi}{2}$$

• $$x=\frac{3\pi}{2}$$

• $$x=2\pi$$