Free Printable Pre-Calculus: Solving Trigonometric Equations

1.

$\frac{\pi}{6}$ is a possible solution to the equation $2\sin^2\alpha+3\sin\alpha-2=0$

a)

True

b)

False

2.

Solve the trigonometric equation:

4\sin^2\left(x\right)-3=0

a)

$\frac{\pi}{3},\frac{2\pi}{3},\frac{4\pi}{3},\frac{5\pi}{3}$

b)

$\frac{\pi}{4},\frac{3\pi}{4},\frac{5\pi}{4},\frac{7\pi}{4}$

c)

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

d)

$0,\ \frac{\pi}{2},\frac{3\pi}{2}$

3.

Solve the trigonometric equation:

2\cos\left(x\right)+\sqrt{2}=0

a)

$\frac{3\pi}{4},\frac{5\pi}{4}$

b)

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

c)

$\frac{5\pi}{4},\frac{7\pi}{4}$

d)

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

4.

Solve the following trigonometric equation:

\sec\left(x\right)+2=0

a)

$\frac{\pi}{3},\frac{5\pi}{3}$

b)

$\frac{2\pi}{3},\frac{4\pi}{3}$

c)

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

d)

$0,\pi$

5.

Solve the trigonometric function:

-2-3\sin\left(x\right)=1-6\sin\left(x\right)

a)

$0$

b)

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

c)

$\frac{\pi}{2}$

d)

$\frac{\pi}{4}$

6.

Solve the trigonometric equation:

\tan^2\left(x\right)+2\tan\left(x\right)=-1

a)

$\frac{\pi}{4},\frac{5\pi}{4}$

b)

$\frac{2\pi}{3},\frac{5\pi}{3}$

c)

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

d)

$\frac{3\pi}{4},\frac{7\pi}{4}$

7.

Solve the trigonometric equation:

\sec\left(x\right)\csc\left(x\right)-2\sec\left(x\right)+\csc\left(x\right)=\csc\left(x\right)

a)

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

b)

$\frac{2\pi}{3},\frac{5\pi}{3}$

c)

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

d)

$0,\pi$

8.

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

a)

$\frac{\pi}{3}$

b)

$\frac{\pi}{6}$

c)

$-\frac{\pi}{3}$

d)

$-\frac{\pi}{6}$

9.

The value of $\cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)\$ is

a)

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

b)

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

c)

$\frac{\pi}{6}$

d)

$-\frac{\pi}{6}$

10.

csc^-1(-√(2))

a)

π/4

b)

3π/4

c)

-π/4

d)

-3π/4

11.

Find the exact value of $\cos^{-1}\left(\frac{\sqrt{3}}{2}\right)$

a)

$-\frac{\pi}{3}$

b)

$\frac{\pi}{3}$

c)

$-\frac{\pi}{6}$

d)

$\frac{\pi}{6}$

12.

Find the exact value of $\sec^{-1}\left(-2\right)$

a)

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

b)

$-\frac{\pi}{3}$

c)

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

d)

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

13.

Arcsin(0)

a)

0

b)

1

c)

1/2

d)

3/2

14.

Arcsin (-1)

a)

π/2

b)

-1

c)

-π/2

d)

1

Pre-Calculus: Solving Trigonometric Equations

Total questions: 14

Worksheet time: 12mins

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