Free Printable Unit 6 Review

1.

Which is the reference angle of $\theta=-135\degree$ ?

No Calculator!

a)

$30\degree$

b)

$45\degree$

c)

$60\degree$

d)

$225\degree$

2.

Which is the reference angle of $\theta=\frac{11\pi}{3}$ ?

No Calculator!

a)

$\frac{\pi}{3}$

b)

$\frac{\pi}{4}$

c)

$\frac{\pi}{6}$

d)

$\frac{12\pi}{3}$

3.

$\tan\left(-210\degree\right)=?$

No Calculator!

a)

$\frac{1}{2}$

b)

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

c)

$\frac{1}{-\sqrt{3}}$

d)

$150\degree$

4.

$\cos\left(\frac{4\pi}{3}\right)=?$

No Calculator!

a)

$\frac{-1}{2}$

b)

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

c)

$-\sqrt{3}$

d)

$\frac{\pi}{3}$

5.

What is the reference angle for 240°?

No Calculator!

a)

60°

b)

30°

c)

45°

d)

210°

6.

What is the reference angle for 63°?

No Calculator!

a)

117°

b)

207°

c)

63°

d)

153°

7.

What is 120 degrees in radians?

No Calculator!

a)

2π/3

b)

π/3

c)

5π/3

d)

4π/3

8.

What is the reference angle for 11π/6?

No Calculator!

a)

π/6

b)

π/3

c)

2π/6

d)

5π/6

9.

What is the reference angle for 2π/3?

No Calculator!

a)

π/4

b)

7π/6

c)

4π/3

d)

π/3

10.

What quadrant is 7π/3?

No Calculator!

a)

I

b)

II

c)

III

d)

^IV

11.

Find the reference angle for an angle measuring -310⁰

No Calculator!

a)

50⁰

b)

-50⁰

c)

20⁰

d)

40⁰

12.

Which trigonometric function would you use to find "h", the height of the tree?

a)

sine

b)

cosine

c)

tangent

d)

none of these

13.

Choose the quadrant where both the tangent and cosine functions produce a negative value.

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

d)

Quadrant 4

14.

In which quadrant is sine positive and secant negative?

a)

Quadrant 1

b)

Quadrant 2

c)

Quadrant 3

d)

Quadrant 4

15.

What is the reference angle?

a)

48

b)

138

c)

132

d)

42

16.

What is the reference angle?

a)

7

b)

63

c)

277

d)

97

17.

sin 60 $\degree$ =?

No Calculator!

a)

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

b)

1

c)

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

d)

$\frac{1}{2}$

18.

sin(0°)=?

No Calculator!

a)

0

b)

1/2

c)

-1

d)

1

19.

Name the quadrant in which ∠A lies, if cosA > 0, sinA < 0

a)

1

b)

2

c)

3

d)

4

20.

Find the value tan θ if cos θ = $\frac{7}{8}$

No Calculator!

a)

$\frac{\sqrt{15}}{8}$

b)

$\frac{7\sqrt{15}}{15}$

c)

$\frac{\sqrt{15}}{7}$

d)

$\frac{8}{7}$

21.

Given the ordered pair (24, 7), find $\csc\theta$ .

No Calculator!

a)

$\frac{25}{24}$

b)

$\frac{7}{25}$

c)

$\frac{25}{7}$

d)

$\frac{17}{15}$

22.

Given the ordered pair (15, 8), find $\tan\theta$

No Calculator!

a)

$\frac{17}{15}$

b)

$\frac{4}{3}$

c)

$\frac{17}{8}$

d)

$\frac{8}{15}$

23.

What is the reference angle?

a)

115

b)

65

c)

25

d)

155

24.

Let (-4, 3) be a point on the terminal side of θ. Which of the following is FALSE?

a)

cot θ = -4/3

b)

tan θ = -3/4

c)

sin θ = 3/5

d)

cos θ = 4/5

25.

If tanθ = -¾ and cscθ > 0, then secθ =

a)

-4/5

b)

5/4

c)

-5/4

d)

4/5

26.

If sinθ = -5/13 and tanθ > 0, then cosθ =

a)

13/12

b)

-13/12

c)

12/13

d)

-12/13

27.

Find $\cot\theta$ if $\sin\theta=\frac{3}{5}$ and $0<\theta<\frac{\pi}{2}$

a)

$\cot\theta=\frac{3}{4}$

b)

$\cot\theta=\frac{4}{5}$

c)

$\cot\theta=\frac{4}{3}$

d)

$\cot\theta=\frac{5}{4}$

28.

Find $\cos\theta$ if $\csc\theta=\frac{13}{5}$ and $\frac{\pi}{2}<\theta<\pi$

a)

$\cos\theta=-\frac{\sqrt{194}}{13}$

b)

$\cos\theta=\frac{13}{12}$

c)

$\cos\theta=\frac{-5}{\sqrt{194}}$

d)

$\cos\theta=-\frac{12}{13}$

29.

Given $\tan\theta=-\frac{15}{8}$ and $\frac{\pi}{2}<\theta<\pi$ , choose those with the correct trig ratio.

a)

$\csc\theta=\frac{17}{15}$

b)

$\cos\theta=\frac{15}{17}$

c)

$\sec\theta=-\frac{17}{8}$

d)

$\sin\theta=-\frac{8}{17}$

30.

Find without a calculator.

a)

-1 / 2

b)

√3 / 2

c)

-√3 / 2

d)

1 / 2

31.

Find the exact value of sin(300⁰).

No Calculator!

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

32.

What is the reference angle for $\frac{4\pi}{3}$ ?

No Calculator!

a)

$\frac{\pi}{3}$

b)

$\frac{\pi}{6}$

c)

$\frac{\pi}{4}$

d)

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

33.

What is the reference angle for -30°?

No Calculator!

a)

150°

b)

30°

c)

80°

d)

60°

34.

What is the reference angle for 125°?

No Calculator!

a)

235°

b)

125°

c)

75°

d)

55°

35.

Find $\sin\left(\theta\right)$ given that $\cot\left(\theta\right)=-\frac{\sqrt{2}}{5}$ and $\cos\left(\theta\right)>0$ .

a)

$-\frac{5\sqrt{3}}{9}$

b)

$\frac{\sqrt{6}}{3}$

c)

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

d)

$-\frac{5}{9}$

36.

Find $\tan\left(\theta\right)$ given that $\sin\left(\theta\right)=-\frac{3}{5}$ and $\cos\left(\theta\right)>0$ .

a)

$-\frac{3}{4}$

b)

$\frac{4}{5}$

c)

$\frac{4}{3}$

d)

$-\frac{5}{3}$

37.

Find sec(θ) given that the terminal side of θ contains the point $\left(\sqrt{5},2\right)$ .

a)

$\frac{3\sqrt{5}}{5}$

b)

$\frac{3}{2}$

c)

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

d)

$-\frac{\sqrt{5}}{3}$

38.

Find sin(θ) given that the terminal side of θ contains the point (-19, 19).

a)

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

b)

$-1$

c)

$-\sqrt{2}$

d)

$-\frac{\sqrt{2}}{19}$

39.

tan 2π = ?

(Find without a calculator.)

a)

0

b)

1

c)

-1

d)

undefined

40.

Find the exact value of this trig function. No Calculator!

a)

1

b)

0

c)

-1

d)

undefined

e)

The correct answer is not listed

41.

What is the reference angle for $\frac{5\pi}{4}$ ?

No Calculator!

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{2}$

c)

$\frac{\pi}{3}$

d)

$\frac{\pi}{6}$

42.

Find the reference angle for $\frac{11\pi}{5}$ .

No Calculator!

a)

$\frac{\pi}{2}$

b)

$\frac{\pi}{3}$

c)

$\frac{\pi}{4}$

d)

$\frac{\pi}{5}$

43.

Evaluate the trigonometric function of the quadrant angle:

\sec\ \pi

a)

0

b)

1

c)

undefined

d)

-1

44.

Find the value of cot θ given that:

\csc\ \theta\ =\ 4\ and\ \cot\theta<0

a)

$-\frac{\sqrt{15}}{15}$

b)

$-\frac{\sqrt{15}}{4}$

c)

$\frac{1}{4}$

d)

$-\sqrt{15}$

45.

Find sin θ given that:

$\cot\theta=-3,\ in\ Quadrant\ II$

a)

$-\frac{\sqrt{10}}{3}$

b)

$\frac{\sqrt{10}}{10}$

c)

$-\frac{3\sqrt{10}}{10}$

d)

$-\frac{1}{3}$

46.

The distance along an arc measured in linear units.

a)

area of a sector

b)

arc length

c)

arc of a circle

d)

sector of a circle

47.

A region bounded by two radii of the circle and their intercepted arc is a ....

a)

arc of a circle

b)

arc length of a circle

c)

sector of a circle

d)

segment of a circle

48.

Find the area of the shaded sector of circle O. The radius is 6 inches and the central angle is 100°. Express answer to the nearest tenth of a square inch.

a)

9.2 sq. in.

b)

10.5 sq. in.

c)

31.4 sq. in.

d)

38.2 sq. in.

49.

Find the area of the dark blue sector shown at the left. The radius of the circle is 4 units and the length of the arc (the curved edge of the sector) measures 7.85 units. Express answer to thenearest tenth of a square unit.

a)

0.3 square units

b)

15.7 square units

c)

19.7 square units

d)

50.3 square units

50.

Find the area of the shaded sector of the circle with a diameter of 30 m.

a)

b)

c)

d)

51.

Find the area of the sector. Round your answer to the nearest tenth.

a)

3.1 yd²

b)

28.3 yd²

c)

6.3 yd²

d)

32.4 yd²

52.

Find the arc length of the sector.

a)

A

b)

B

c)

C

d)

D

53.

Find the radius of Circle R.

a)

$4$

b)

$\frac{45}{2}$

c)

$45\pi$

d)

$7$

54.

The Sector Area is $54\pi$ . What is the radius?

a)

$120\degree$

b)

81

c)

9

d)

$240\degree$

55.

The length of an arc with central angle $90\degree$ is $10\pi$ cm. What is the RADIUS of the circle?

a)

40 cm

b)

20 cm

c)

10 cm

d)

5 cm

56.

What is the radian equivalent of -460 degrees?

(Find without a calculator.)

a)

$\frac{9\pi}{23}$

b)

$\frac{23\pi}{9}$

c)

$-\frac{23\pi}{9}$

d)

$-\frac{9\pi}{23}$

57.

Which of the following is equivalent to $89^o11'15"$ ?

a)

89.5 degrees

b)

89.4 degrees

c)

89.1 degrees

d)

89.2 degrees

58.

Which angle is coterminal to 480 degrees?

(Find without a calculator.)

a)

-480 degrees

b)

60 degrees

c)

120 degrees

d)

280 degrees

59.

Convert the angle to degrees, minutes and seconds.

a)

b)

c)

d)

60.

Convert 173.459º to Degrees, Minutes, Seconds

a)

173º 27' 32.4"

b)

173º 27' 324"

c)

173º 32' 27"

d)

173º 324' 27"

61.

Convert 163º 24' 28" to Degrees

a)

163.4567º

b)

163.5789º

c)

163.2091º

d)

163.4078º

62.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

63.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

64.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

65.

Which Law would you use?

a)

Law of Sines

b)

Law of Cosines

c)

Law of the Jungle

d)

Law of Gravity

66.

What is the measure of angle A?

a)

50 degrees

b)

60 degrees

c)

78 degrees

d)

74 degrees

67.

What is the length of side x?

a)

130 cm

b)

112 cm

c)

150 cm

d)

105 cm

68.

Based on the given information determine the number of unique triangles that may exist.
A = 98°, a = 29, b = 6

a)

1 Triangle

b)

2 Triangles

c)

No Triangles

d)

3 Triangles

69.

Based on the given information determine the number of unique triangles that may exist.
A= 37°, a=8, b=14

a)

1 Triangle

b)

2 Triangles

c)

No Triangles

d)

3 Triangles

70.

Based on the given information determine the number of unique triangles that may exist.
B= 70°, b=85, c=88

a)

1 Triangle

b)

2 Triangles

c)

No Triangles

d)

3 Triangles

71.

Use Law of Cosines to find XZ

a)

16.004 meters

b)

544.165 meters

c)

34.7 meters

d)

1204.165 meters

72.

What is the length of side x?

a)

6.57 cm

b)

7 cm

c)

7.44 cm

d)

26.33 cm

73.

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

74.

Parker must find the distance from Point A to Point B on opposite sides of a lake. He locates Point C that is 860 feet from point A and 175 feet from Point B. He measures the angle at Point C to be 78 degrees. Find the distance from point A to point B.

a)

707643.58

b)

841.22

c)

877.62

d)

842.01

75.

Amanda and Jamie are standing 25 feet apart and spot a bird in the sky between them. The angle of elevation from Amanda to the bird is 55, and from Jamie to the bird is 63. How far away is the bird from Amanda?

a)

25.23

b)

23.19

c)

22.15

d)

20.85

76.

Find the length of Side BC.

a)

33

b)

24

c)

12

d)

29

77.

Using Hero's Formula, find the Area.

a)

56

b)

28

c)

24.2

d)

104.4

78.

Using Hero's Formula, find the Area.

a)

35

b)

49

c)

28.9

d)

27.8

79.

Find the area of ABC to the nearest tenth.

a)

62.3 units²

b)

124.6 units²

c)

77.0 units²

d)

100 units²

80.

What is the area of a triangle with two sides that measure 6 m and 8 m with an included angle of 137°?

a)

17.8m²

b)

14.6m²

c)

16.4m²

d)

12.9m²

Unit 6 Review

Total questions: 80

Worksheet time: 5hrs 49mins

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