Free Printable Trigonometric Equations

1.

Solve
sinθ = √3/2

a)

θ = π /6, 5π /6

b)

θ = 2π /3, 4π /3

c)

θ = π /3, 2π /3

d)

θ = π /4, 3π /4

2.

Solve the trigonometric equation in the interval $\left(0,\ 2\pi\right]$ .

$11\sin x+5=\sin x$

a)

$\frac{\pi}{3},\frac{2\pi}{3}$

b)

$\frac{\pi}{6},\frac{5\pi}{6}$

c)

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

d)

$\frac{\pi}{6},\frac{5\pi}{6},\frac{7\pi}{6},\frac{11\pi}{6}$

3.

Solve on the domain [0,2π)
cos x + 1 = 0

a)

0

b)

No solution

c)

π

d)

3π/2

4.

Solve on the Interval [0,2π)
sinθ = -1

a)

θ = π /2, 3π /2

b)

θ = π /2

c)

θ = 3π /2

d)

θ = π

5.

Solve for x: $5\cos x+\sqrt{2}=3\cos x$

a)

$\pi$

b)

$\frac{3\pi}{4}$

c)

DNE

d)

$\frac{4\pi}{3}$

6.

Solve the equation: $4\sqrt[]{2}=8\cos\theta$ for 0 ≤ θ < 2π.

a)

π/4, 11π/6

b)

π/4, 7π/4

c)

π/6, π/4

d)

7π/4, 11π/4

7.

Solve the equation: $5+\sin\theta=\frac{11}{2}$ for 0 ≤ θ < 2π.

a)

π/6, 11π/6

b)

π/6, 7π/6, 11π/6

c)

11π/6

d)

π/6, 5π/6

8.

Solve the equation: $3-8\cos\theta=-1$ for 0 ≤ θ < 2π.

a)

5π/4

b)

π/3, 5π/3

c)

No solution.

d)

5π/3

9.

Solve the equation: $5=3-4\sin\theta$ for $0\le\theta<2\pi$

a)

No solution.

b)

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

c)

$\frac{11\pi}{6}$

d)

$\frac{7\pi}{6},\frac{7\pi}{4},\frac{11\pi}{6}$

10.

Solve the equation: $3-8\cos\theta=-1$ for 0 ≤ θ < 2π.

a)

5π/4

b)

π/3, 5π/3

c)

No solution.

d)

5π/3

Trigonometric Equations

Total questions: 10

Worksheet time: 32mins

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