Free Printable Precalculus 5.1-5.3 Quiz

1.

Write the following trigonometric expression in terms of sine and cosine, and then simplify: sin x cot x

a)

cot x

b)

1

c)

sin x

d)

cos x

2.

Write the following trigonometric expression in terms of sine and cosine, and then simplify: sin ² x (1 + cot ² x)

a)

cot x

b)

1

c)

sin x

d)

cos x

3.

Simplify the following trigonometric expression:
$\frac{\sec^2x\ -1}{\sec^2x}$

a)

$\sec^2x$

b)

1

c)

$\sin\ x$

d)

$\sin^2x$

4.

Simplify the following trigonometric expression as much as possible:

sin B + cos B cot B

a)

cos B

b)

cot B

c)

sin B

d)

csc B

5.

Simplify the following trigonometric expression: $\frac{\sin x\ \csc\ x}{\cot x}$

a)

$\tan\ x$

b)

$\cot\ x$

c)

1

d)

$\cos\ x$

6.

When verifying the identity: $\left(1-\sin x\right)\left(1+\sin x\right)=\cos^2x$
The first step would be to

a)

Add

b)

Subtract

c)

Substitute

d)

Multiply

7.

When verifying the identity $\left(\tan^2x+1\right)\left(\cos^2x-1\right)=-\tan^2x$
The first step would be:
$\left(\sec^2x\right)\left(-\sin^2x\right)$
The reason for this step is

a)

Pythagorean Identities

b)

Adding

c)

Multiplying

d)

Reciprocal Identities

8.

$\sec\ x\ -\ 2=0$ Which of the following is a solution to the given equation?

a)

$x=\frac{\pi}{4}$

b)

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

c)

$x=\frac{7\pi}{4}$

d)

$x=\frac{5\pi}{3}$

e)

$x=\frac{7\pi}{6}$

9.

Solve the following equation, for all real numbers.
$\sin^2x+\sin x\ =0$

a)

$x=n\pi\ \ and\ \$

$x=\frac{3\pi}{4}+n\pi$

b)

$x=n\pi\ \ and\$

$\ x=\frac{3\pi}{2}+n\pi$

c)

$x=n\pi\ \ and\$

$\ x=\frac{\pi}{2}+n\pi$

d)

$x=n\pi\ \ and\$

$\ x=\frac{3\pi}{2}+2n\pi$

e)

$x=\frac{2\pi}{3}+2n\pi\ \ and\$

$\ x=\frac{5\pi}{3}+2n\pi$

10.

Solve the multiple-angle equation.
$\cos\ \frac{x}{2}=-\frac{\sqrt{3}}{2}$

a)

$x=\frac{5\pi}{3}+4\pi n\ and$

$\ x=\frac{7\pi}{3}+4\pi n$

b)

$x=\frac{2\pi}{3}+2\pi n\ and$

$\ x=\frac{5\pi}{3}+2\pi n$

c)

$x=\frac{5\pi}{6}+2\pi n\ and\$

$x=\frac{7\pi}{6}+2\pi n$

d)

$x=\frac{7\pi}{6}+2\pi n\ and$

$\ x=\frac{11\pi}{6}+2\pi n$

e)

$x=\frac{5\pi}{3}+2\pi n\ and$

$\ x=\frac{8\pi}{3}+2\pi n$

Precalculus 5.1-5.3 Quiz

Total questions: 10

Worksheet time: 30mins

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