Free Printable Trigonometry Review I

1.

Find the length of side y.

a)

22.32 cm

b)

36.5 cm

c)

76.34 cm

d)

87.76 cm

2.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

3.

Find the length of side w.

a)

21.4 cm

b)

18.0 cm

c)

36.5 cm

d)

43.6 cm

4.

Find the measure of the indicated angle (?) round to the nearest tenth.

a)

9.4

b)

55.2

c)

20.15

d)

19.4

5.

Choose the correct set up to find the length of the side x.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

6.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

7.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

8.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

9.

What is the length of side x?

a)

130 cm

b)

112 cm

c)

150 cm

d)

105 cm

10.

Find the measure of ∠A

a)

18

b)

28

c)

25

d)

24

11.

Clint is building a wooden swing set for his children. Each supporting end of the swing set is to be an A-frame constructed with two 10 foot long 4-by-4s joined at a 45 degree angle. To prevent the swing set form tipping over, Clint wants to secure the base of each A-frame to concrete footings. How far apart should the footings for each A-frame be?

a)

5.461 feet

b)

9.743 feet

c)

6 feet

d)

7.65 feet

12.

Jack is flying his kite. He runs 100 feet away from his house and lets out 75 feet of string. The angle of elevation from the ground to the kite is 65 degrees. How far away is the kite from the house?

a)

9285.73 ft

b)

96.36 ft

c)

24061.81 ft

d)

155.12 ft

13.

How many triangles can you make if A=53, b=6, and a=5?

a)

0

b)

1

c)

2

d)

Infinitely many

14.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

15.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

16.

cos 4π/3

a)

-√3/2

b)

√3/2

c)

1/2

d)

-1/2

17.

sin 2π/3

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

18.

What is the exact coordinates of 3π/4 on the unit circle?

a)

(−√2∕2, √2∕2)

b)

(−√2∕2, −√2∕2)

c)

(−√3∕2, −√2∕2)

d)

(√2∕2, −√2∕2)

19.

a)

-√3/2

b)

-½

c)

-√2/2

d)

-1

20.

a)

1

b)

-1

c)

0

d)

√2/2

21.

a)

√3/3

b)

√3

c)

1

d)

undefined

22.

a)

-1

b)

0

c)

undefined

d)

√3

23.

a)

½

b)

√2/2

c)

√3/2

d)

1

24.

What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

25.

What is the vertical shift?

a)

Down 1

b)

Down 5

c)

Down 3

d)

Down 4

26.

Determine an equation for this graph:

a)

y=csc(x)

b)

y=sec(x)

c)

y=cot(x)

d)

y= tan(x)

27.

What is the maximum value of the wave y = 10sin(2x - 20) + 25?

a)

10

b)

20

c)

35

d)

30

28.

The following wave represents a sound recorded for 8s. Which equation best represents this wave?

a)

S = 5sin(2x)

b)

S = sin(5x)

c)

S = 5sin(180x)

d)

S = 180sin(5x)

29.

Which is an equation of the cosine function with an amplitude of 2, period of Π, phase shift of Π/2?

a)

y= -2cos(x/2 - ∏/4)

b)

y= 2cos (x/2 + ∏)

c)

y= 2cos (2x-∏)

d)

y= -2cos(2x-∏/2)

30.

What is the phase shift for y = 4cos(¹/₂x +π) - 2?

a)

left pi/2

b)

right pi/2

c)

right 2pi

d)

left 2pi

31.

What is the equation of the graph?

a)

y = 2 cos x

b)

y = sin x

c)

y = 2 sin x

d)

y = sin 2x

32.

What is the equation of the graph?

a)

y = -2 cos x - 3

b)

y = 3 cos x - 2

c)

y = -7 cos x - 3

d)

y = -3 cos x - 4

33.

3. Determine an equation for this graph:

a)

y=csc(x)

b)

y=sec(x)

c)

y=cot(x)

d)

y= tan(x)

34.

4. Determine an equation for this graph:

a)

y=csc(x)

b)

y=sec(x)

c)

y=cot(x)

d)

y= tan(x)

35.

9. What is the amplitude for y = 4cos(¹/₂x +π) - 2?

a)

2

b)

pi/2

c)

pi

d)

4

36.

What is the amplitude of

y = -3sin (7x) -2

a)

7

b)

-2

c)

3

d)

-3

37.

What is the period?

a)

4π

b)

2π

c)

π

d)

8π

38.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$\tan\theta=-\sqrt{3}$

a)

$60\degree$

b)

$120\degree$

c)

$240\degree$

d)

$300\degree$

39.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$6\sin\theta=3$

a)

$60\degree$

b)

$300\degree$

c)

$30\degree$

d)

$150\degree$

40.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$4\cos\theta=-2$

a)

$60\degree$

b)

$120\degree$

c)

$240\degree$

d)

$300\degree$

41.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$5+\tan\theta=4$

a)

$45\degree$

b)

$135\degree$

c)

$225\degree$

d)

$315\degree$

42.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$-12-3\tan\theta=-12+\sqrt{3}$

a)

$30\degree$

b)

$150\degree$

c)

$210\degree$

d)

$330\degree$

43.

Solve the equation for $0\degree\le\theta\le360\degree$ . Select ALL correct answers.

$\sin\theta\tan\theta-\sqrt{3}\sin\theta=0$

a)

$0\degree$

b)

$60\degree$

c)

$180\degree$

d)

$240\degree$

e)

$360\degree$

44.

Find the general solution of the equation.

a)

π/4+2πpn

b)

π/4+2πn; 7π/4+2πpn

c)

7π/4+2πpn

d)

π/4, 7π/4

45.

Find the general solution of the equation.

a)

0

b)

2π

c)

2πn

d)

No Solution

46.

Find the general solution of the equation.

a)

π/6+2πn; 11π/6+2πn

b)

π/6+2πn

c)

11π/6+2πn

d)

π/6; 11π/6

47.

Find the general solution of the equation.

a)

π/6+2πn

b)

5π/6+2πn

c)

π/6; 5π/6

d)

π/6+2πn; 5π/6+2πn

48.

Find the solution on the interval [0, 2π)

a)

π/6; 5π/6; 7π/6; 11π/6

b)

π/6; 5π/6

c)

7π/6; 11π/6

d)

π/6+2πn; 5π/6+2πn

49.

Find the solution on the interval [0, 2π)

a)

0; π

b)

π; π/4; 3π/4; 5π/4; 7π/4

c)

0; π; π/4; 3π/4; 5π/4; 7π/4

d)

No Solution

50.

Which feature of the graph corresponds to the highlighted segment?

a)

Amplitude

b)

Period

c)

Midline

51.

Which feature of the graph corresponds to the highlighted segment?

a)

Amplitude

b)

Period

c)

Midline

52.

sin^-1(-1/2) (Make sure you are working with radians when using Desmos graphing calculator remember pi=3.14)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

53.

What are the domain and range of y = arcsin(x)

a)

domain [-1, 1] range [-2π, 2π]

b)

domain [-1, 1] range [0, π]

c)

domain [-1, 1] range [-π/2, π/2]

d)

domain [0,2π] range [-1, 1]

54.

What are the domain and range of y = arccos(x)

a)

domain [-1, 1] range [-2π, 2π]

b)

domain [-1, 1] range [0, π]

c)

domain [-1, 1] range [-π/2, π/2]

d)

domain [0, 2π] range [-1, 1]

55.

What are the domain and range of y = arctan(x)

a)

domain [-1, 1] range [-2π, 2π]

b)

domain (-∞, ∞) range [-π/2, π/2]

c)

domain [-1, 1] range (-π/2, π/2)

d)

domain (-∞, ∞) range (-π/2, π/2)

56.

What is the quadrant II answer for Ɵ, is sin Ɵ = 0.7193

a)

146^o

b)

134^o

c)

126^o

d)

136^o

57.

$In\ what\ quadrants\ can\ \sin\theta=\cos\theta?\ You\ may\ have\ more\ than\ one\ answers\ checked$

a)

I

b)

II

c)

III

d)

IV

58.

What quadrants are the domain for inverse sin?

a)

I

b)

II

c)

III

d)

IV

59.

What quadrants are the domain for inverse tan?

a)

I

b)

II

c)

III

d)

IV

60.

What quadrants are the domain for inverse cosine?

a)

I

b)

II

c)

III

d)

IV

Trigonometry Review I - Precalculus

Total questions: 60

Worksheet time: 4hrs 38mins

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