Free Printable OnRamps Unit 4A Review

1.

Using the given triangle, find the cos(A)

a)

$\frac{1}{\sqrt{5}}$

b)

$2$

c)

$\frac{2}{\sqrt{5}}$

d)

$6$

2.

Using the given triangle, find the cot(A)

a)

$\frac{1}{2}$

b)

$2$

c)

$\frac{2}{\sqrt{5}}$

d)

$\frac{1}{\sqrt{5}}$

3.

Using the given triangle, find the csc(A)

a)

$\frac{1}{2}$

b)

$12$

c)

$\frac{\sqrt{5}}{2}$

d)

$\sqrt{5}$

4.

Given that $\cos\left(\theta\right)=\frac{24}{25}$ , find $\sin\left(\theta\right)$

a)

$\frac{7}{25}$

b)

$\frac{24}{25}$

c)

$\frac{25}{7}$

d)

$\frac{25}{24}$

5.

Given that $\cos\left(\theta\right)=\frac{24}{25}$ , find $\cot\left(\theta\right)$

a)

$\frac{7}{25}$

b)

$\frac{24}{7}$

c)

$\frac{25}{7}$

d)

$\frac{7}{24}$

6.

Solve for a. You may use a calculator.

a)

12

b)

8.9

c)

0.06

d)

7.2

7.

Solve for B. You may use a calculator.

a)

31

b)

121

c)

59

8.

A 25-ft ladder leans against a building so that the angle between the ground and the ladder is 70°.

How high does the ladder reach up the side of the building? You may use a calculator.

a)

23.5 ft

b)

8.6 ft

c)

68.7 ft

d)

25 ft

9.

A radio tower is located 600 feet from a building. From a window in the building, a person determines that the angle of depression to the bottom of the tower is 40° and that the angle of elevation to the top of the tower is 19°. How tall is the tower? You may use a calculator.

a)

710 ft

b)

2457.6 ft

c)

206.6 ft

d)

1742.5 ft

10.

Find the length x. You may use a calculator.

a)

124.7

b)

150.1

c)

45.9

11.

Convert the angle 90° to radians.

a)

$\frac{\pi}{2}$

b)

$\pi$

c)

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

d)

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

12.

Convert the angle 36° to radians.

a)

$\frac{\pi}{5}$

b)

$\frac{\pi}{3}$

c)

$\frac{\pi}{6}$

d)

$\frac{\pi}{10}$

13.

Convert the angle $\frac{2\pi}{3}$ from radians to degrees.

a)

120

b)

60

c)

270

14.

Convert the angle $\frac{5\pi}{12}$ from radians to degrees.

a)

75

b)

0.42

15.

Simplify to an expression containing one trig function and no fractions.
$\csc\theta\cdot\tan\theta$

a)

$\sec\theta$

b)

$\cos\theta$

c)

$\sin\theta$

d)

$\csc\theta$

16.

Simplify to an expression containing one trig function and no fractions.
$\frac{\sec\theta}{\csc\theta}$

a)

$\tan\theta$

b)

$\cot\theta$

c)

$\sin\theta$

d)

$1$

17.

Simplify to an expression containing one trig function and no fractions.
$\frac{\cot\theta}{\csc\theta}$

a)

$\tan\theta$

b)

$\cos\theta$

c)

$\sin\theta$

d)

$\sec\theta$

18.

Simplify to an expression containing one trig function and no fractions.
$\frac{\sin^2\theta+\cos^2\theta}{\cos^2\theta}$

a)

$\sec^2\theta$

b)

$\tan^2\theta$

c)

$\cos^2\theta$

d)

$\csc^2\theta$

19.

Simplify to an expression containing one trig function and no fractions.
$\sec\theta\cdot\tan\theta\cdot\cos\theta$

a)

$\sin\theta$

b)

$\tan\theta$

c)

$\cos^2\theta$

d)

$1$

20.

Simplify to an expression containing one trig function and no fractions.
$\frac{\cos^2\theta-1}{1-\sin^2\theta}$

a)

$\cot^2\theta$

b)

$\tan^2\theta$

c)

$-\tan^2\theta$

d)

$-\cot^2\theta$

21.

Which of the following angles is coterminal with $645\degree$ ?

a)

$285\degree$

b)

$465\degree$

c)

$-645\degree$

d)

$45\degree$

22.

Which of the following angles is NOT coterminal with $43\degree$ ?

a)

$137\degree$

b)

$403\degree$

c)

$1123\degree$

d)

$-317\degree$

23.

Which of the following angles is NOT coterminal with $-\frac{7\pi}{2}$ ?

a)

$\frac{7\pi}{2}$

b)

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

c)

$\frac{\pi}{2}$

d)

$\frac{41\pi}{2}$

24.

Which of the following angles is coterminal with $\frac{3\pi}{4}$ ?

a)

$\frac{11\pi}{4}$

b)

$\frac{\pi}{4}$

c)

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

d)

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

25.

Using your unit circle, evaluate the following expression:

\cos\left(\frac{\pi}{3}\right)

a)

$\frac{1}{2}$

b)

$\frac{\sqrt{3}}{2}$

c)

$\frac{\sqrt{2}}{2}$

d)

$\frac{\pi}{3}$

26.

Using your unit circle, evaluate the following expression:
$\sin\left(\frac{\pi}{4}\right)$

a)

$\frac{\sqrt{2}}{2}$

b)

$\frac{\sqrt{3}}{2}$

c)

$\frac{1}{2}$

d)

$1$

27.

Using your unit circle, evaluate the following expression:
$\sin\left(\pi\right)$

a)

$1$

b)

$0$

c)

$-1$

d)

$\frac{1}{2}$

28.

Using your unit circle, evaluate the following expression:
$\tan\left(\frac{4\pi}{3}\right)$

a)

$\sqrt{3}$

b)

$\frac{\sqrt{3}}{3}$

c)

$-\sqrt{3}$

d)

$-\frac{\sqrt{3}}{3}$

29.

Using your unit circle, evaluate the following expression:
$\cos\left(\frac{4\pi}{3}\right)$

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

$-\frac{\sqrt{2}}{2}$

30.

Using your unit circle, evaluate the following expression:
$\cot\left(0\right)$

a)

$0$

b)

undefined

c)

$1$

d)

$-1$

31.

Using your unit circle, evaluate the following expression:
$\csc\left(\frac{7\pi}{6}\right)$

a)

$-2$

b)

$-\frac{1}{2}$

c)

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

d)

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

32.

Using your unit circle, evaluate the following expression:
$\sec\left(\frac{\pi}{6}\right)$

a)

$\frac{2\sqrt{3}}{3}$

b)

$\frac{\sqrt{3}}{2}$

c)

$\frac{1}{2}$

d)

$2$

33.

Using your unit circle, evaluate the following expression:
$\cos\left(\pi\right)$

a)

$-1$

b)

$1$

c)

$0$

d)

$\frac{1}{2}$

34.

Using your unit circle, evaluate the following expression:
$\csc\left(\frac{5\pi}{4}\right)$

a)

$-\sqrt{2}$

b)

$-\frac{\sqrt{2}}{2}$

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

35.

Using your unit circle, evaluate the following expression:
$\tan\left(\frac{\pi}{4}\right)$

a)

$1$

b)

$-1$

c)

$2$

d)

$0$

36.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\sin\theta=\frac{\sqrt{2}}{2}$

a)

$\frac{\pi}{4}$

b)

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

c)

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

d)

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

37.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\tan\theta=-1$

a)

$\frac{\pi}{4}$

b)

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

c)

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

d)

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

38.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\cos\theta=0$

a)

$0$

b)

$\frac{\pi}{2}$

c)

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

d)

$\pi$

39.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\tan\theta=undefined$

a)

$0$

b)

$\frac{\pi}{2}$

c)

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

d)

$\pi$

40.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\cot\theta=-\sqrt{3}$

a)

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

b)

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

c)

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

d)

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

41.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\sec\theta=-1$

a)

$0$

b)

$\frac{\pi}{2}$

c)

$\pi$

d)

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

42.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$2\sin\theta=-1$

a)

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

b)

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

c)

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

d)

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

43.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\sin^2\theta=\frac{1}{4}$

a)

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

b)

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

c)

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

d)

$\frac{\pi}{6}$

44.

Solve the trig equation using the unit circle. Answers should be $0\le\theta<2\pi$ . There may be more than one correct answer.
$\csc\left(2\theta\right)-2=0$

a)

$\frac{\pi}{12}$

b)

$\frac{5\pi}{12}$

c)

$\frac{13\pi}{12}$

d)

$\frac{17\pi}{12}$

45.

Which of the following is NOT a solution to the trig equation?
$2\sin\theta\cos\theta=\cos\theta$

a)

$\frac{\pi}{2}$

b)

$\frac{\pi}{6}$

c)

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

d)

$\pi$

46.

Which of the following is NOT a solution to the trig equation?
$\tan\theta\sin\theta-\sin\theta=0$

a)

$\frac{\pi}{2}$

b)

$\pi$

c)

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

d)

$\frac{\pi}{4}$

47.

Which of the following is NOT a solution to the trig equation?
$2\cos^2\theta+3\cos\theta+1=0$

a)

$0$

b)

$\pi$

c)

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

d)

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

OnRamps Unit 4A Review

Total questions: 47

Worksheet time: 12hrs 45mins

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