5.5 Trigonometric Equations

​5.5 Trigonometric Equations

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Multiple Choice

The value of  $$\sin^{-1}\left(-\frac{1}{2}\right)\$$  #39

• $$\frac{\pi}{3}$$  

• $$\frac{\pi}{6}$$  

• $$-\frac{\pi}{3}$$  

• $$-\frac{\pi}{6}$$  

Multiple Choice

Solve sinθ = ½ for all Radian angles between 0 and $$2\pi$$  . #1

• θ = π / 6,  7π / 6

• θ = π / 6,  5π / 6

• θ = 5π / 6,  7π / 6

• θ = 7π / 6,  11π / 6

Multiple Choice

Solve sinθ = -1 for all Radian angles between 0 and $$2\pi$$  . #2

• θ = π /2, 3π /2 

• θ = π /2

• θ = 3π /2

• θ = π  

Multiple Select

Solve for 0≤x≤2π

sinxtanx = sinx #7

• π/2, 3π/2

• 3π/4, 7π/4

• 0, π, 2π

• π/4, 5π/4

Multiple Choice

Solve for 0≤x≤2π

2sin²x - 5sinx + 2 = 0 #8

• π/6, 5π/6

• 7π/6, 11π/6

• π/3, 2π/3

• 4π/3, 5π/3

Multiple Select

Solve for 0≤x≤2π

2sin²x - sinx = 0 #9

• 0, π, 2π

• π/2, 3π/2

• π/6, 5π/6

• π/3, 2π/3

Multiple Choice

Solve for 0≤x≤2π

3sin²x + sinx - 4 = 0 #11

• 0, π

• π/2

• π/6, 5π/6

• 3π/2

Multiple Select

Solve for 0≤x≤2π

2cos²x + 3cosx = -1

• 0, 2π

• π

• 2π/3, 4π/3

• π/3, 5π/3

Multiple Choice

Solve for 0≤x≤2π

tanx = 1 #10

• π/2, π

• π/4, 3π/4

• π/4, 5π/4

• 3π/4, 7π/4

Multiple Select

Which of the following are the correct solutions for the trigonometric equation in the interval  $$\left(0,\ 2\pi\right]$$ ? 

CHOOSE ALL THAT APPLY $$\left(2\sin^2x-1\right)\left(3\tan^2x-1\right)=0$$  #18

• $$\frac{\pi}{4},\frac{3\pi}{4}$$  

• $$\frac{\pi}{6},\frac{5\pi}{6}$$  

• $$\frac{7\pi}{6},\frac{11\pi}{6}$$  

• $$\frac{5\pi}{4},\frac{7\pi}{4}$$  

Multiple Choice

Give a general formula for all solutions to the following equation: $$2\cos x+1=1$$  #33

• $$\frac{\pi}{2}+2\pi k,\ \frac{3\pi}{2}+\pi k$$  

• $$\frac{\pi}{2}+\pi k$$  

• $$\frac{\pi}{3}+2\pi k,\ \frac{4\pi}{3}+2\pi k$$  

• $$\frac{3\pi}{2}+2\pi k$$