Free Printable 10054 Unit 3 Review (Topics 18-23): Trigonometry

1.

How many degrees is ^π/₃ radians?

a)

30°

b)

45°

c)

60°

d)

90°

2.

How many degrees is ^π/₄ radians?

a)

30°

b)

45°

c)

60°

d)

90°

3.

How many degrees is ^π/₂ radians?

a)

30°

b)

45°

c)

60°

d)

90°

4.

How many degrees is ^π/₆ radians?

a)

90°

b)

60°

c)

45°

d)

30°

5.

What is the order of the coordinate pairs for the points on the Unit Circle?

a)

$\left(\tan\theta,\sin\theta\right)$

b)

$\left(\cot\theta,\cos\theta\right)$

c)

$\left(\sin\theta,\cos\theta\right)$

d)

$\left(\cos\theta,\sin\theta\right)$

6.

$\tan\left(\theta\right)$ represents...

a)

the $x$ coordinate on the unit circle

b)

the $y$ coordinate on the unit circle

c)

the ratio of coordinates: $\frac{y}{x}$

7.

$\sin\left(120\degree\right)=$

a)

$\frac{\sqrt[]{2}}{2}$

b)

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

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

8.

$\sin\left(\frac{\pi}{4}\right)=$

a)

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

b)

$\frac{1}{2}$

c)

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

d)

$1$

e)

$0$

9.

Give the exact value of the expression.

\sin\left(-\frac{\pi}{4}\right)

a)

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

b)

$\frac{\pi}{4}$

c)

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

d)

1

10.

Evaluate $\sin\left(\frac{\pi}{2}\right)$

a)

$-\frac{1}{2}$

b)

$\frac{1}{2}$

c)

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

d)

$-1$

e)

$1$

11.

$\sin\left(-\frac{5\pi}{3}\right)$

a)

$\frac{1}{2}$

b)

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

c)

$-\frac{1}{2}$

d)

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

12.

$\sin\left(-135\degree\right)=$

a)

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

b)

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

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

13.

Evaluate:

\sin\left(\frac{3\pi}{2}\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

14.

$\sin\ \frac{15\pi}{4}$

a)

$\frac{1}{2}$

b)

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

c)

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

d)

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

15.

$\cos\left(\frac{7\pi}{6}\right)=$

a)

$\frac{\sqrt[]{2}}{2}$

b)

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

c)

$-\frac{1}{2}$

d)

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

16.

$\cos\left(0\right)=$

a)

$0$

b)

$1$

c)

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

d)

$\frac{1}{2}$

e)

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

17.

Exact value of $\sin\left(-\frac{5\pi}{3}\right)$

a)

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

b)

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

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

18.

Evaluate $\sin\left(\frac{23\pi}{6}\right)$

a)

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

b)

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

c)

$-\frac{1}{2}$

d)

$\sqrt{3}$

19.

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

a)

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

b)

-2

c)

$-\sqrt{2}$

d)

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

20.

$\csc\ \frac{\pi}{3}$

a)

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

b)

2

c)

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

d)

$\frac{1}{2}$

21.

Exact value of $\tan\ \left(\frac{5\pi}{6}\right)$

a)

$-\ \sqrt[]{3}$

b)

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

c)

$\frac{1}{2}$

d)

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

e)

$\frac{\sqrt[]{3}}{3}$

22.

$\tan\ \frac{7\pi}{3}$

a)

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

b)

$\sqrt{3}$

c)

-1

d)

$-\sqrt{3}$

23.

$\sec\ \frac{\pi}{2}$

a)

0

b)

1

c)

undefined

d)

-1

24.

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

a)

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

b)

$\sqrt{3}$

c)

1

d)

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

25.

Give the exact value of the expression.

\cot\left(-\frac{4\pi}{3}\right)

a)

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

b)

$-\sqrt{3}$

c)

$\frac{1}{2}$

d)

$-\frac{1}{2}$

26.

Evaluate:

\tan\left(\frac{3\pi}{2}\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

27.

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

a)

$\frac{\sqrt[]{2}}{2}$

b)

$\frac{\sqrt[]{3}}{3}$

c)

$-\sqrt[]{3}$

d)

$-\frac{1}{2}$

28.

$\tan(-\pi)=$

a)

undefined

b)

0

c)

1

d)

-1

29.

Which of the following equal 0

a)

$\sin\left(0\right)$

b)

$\sec\left(\frac{3\pi}{2}\right)$

c)

$\tan\left(\pi\right)$

d)

$\cot\left(\frac{\pi}{2}\right)$

30.

Which of the following are undefined?

a)

$\sec\left(\frac{\pi}{2}\right)$

b)

$\tan\left(\pi\right)$

c)

$\csc\left(\pi\right)$

d)

$\cot\left(\frac{3\pi}{2}\right)$

31.

Find θ if $\sin\left(\theta\right)=-\frac{\sqrt{3}}{2}$ , and θ is in Quadrant III.

a)

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

b)

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

c)

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

d)

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

32.

Evaluate the given expression using only your unit circle. Give answers in degrees!

\cos^{-1}\left(\frac{-1}{2}\right)

=___

\degree

a)

30

b)

60

c)

120

d)

150

33.

Evaluate the given expression using only your unit circle. Give answers in degrees!

\tan^{-1}\left(-1\right)

=___

\degree

a)

-45

b)

45

c)

315

d)

90

34.

Use the unit circle to match the angle measure: $\cos\left(\frac{10\pi}{3}\right)$

a)

$\frac{\sqrt[]{2}}{2}$

b)

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

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

35.

Evaluate the given expression using only your unit circle. Give answers in degrees!

$\arcsin\left(\frac{1}{2}\right)$ = (a) $\degree$

36.

Evaluate the given expression using only your unit circle. Give answers in degrees!

\sin^{-1}\left(-1\right)

=___

\degree

a)

45

b)

90

c)

0

d)

-90

37.

Find the general solution of the equation.

a)

π/3; 5π/3

b)

2π/3; 4π/3

c)

7π/6; 11π/6

d)

π/6; 5π/6

38.

If the angle $\theta$ is in quadrant II and the $\sin\theta=\frac{5}{7}$ which of the following represents the $\cos\theta$ ?

a)

$\frac{-7}{5}$

b)

$\frac{7}{5}$

c)

$\frac{-2\ \ \sqrt[]{6}}{7}$

d)

$\frac{2\ \sqrt[]{6}}{7}$

39.

What quadrant is $\theta=-\frac{2\pi}{3}$ in?

a)

I

b)

II

c)

III

d)

IV

40.

Give the exact value of the expression.

\sin^{-1}\left(1\right)

a)

1

b)

0

c)

$\pi$

d)

$\frac{\pi}{2}$

41.

Evaluate $Sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)=$

a)

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

b)

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

c)

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

d)

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

e)

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

42.

Give the exact value of the expression.

\tan^{-1}\left(1\right)

a)

$\frac{\pi}{4}$

b)

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

c)

$\frac{\pi}{2}$

d)

0

43.

Evaluate $Cos^{-1}\left(-\frac{1}{2}\right)=$

a)

$\frac{\pi}{4}$

b)

$\frac{\pi}{3}$

c)

$\frac{\pi}{2}$

d)

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

e)

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

44.

Give the exact value of the expression.

\arccos\left(-\frac{1}{\sqrt{2}}\right)

a)

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

b)

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

c)

$\frac{\pi}{4}$

d)

$\frac{\pi}{6}$

45.

Give the exact value of the expression.

\cos^{-1}\left(-1\right)

a)

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

b)

0

c)

$\frac{\pi}{2}$

d)

$\pi$

46.

What is the amplitude of the function $y=3\sin\left(2x-\frac{2\pi}{3}\right)$ ?

Amplitude $=\left|a\right|$

(a)

47.

What is the period of the function $y=3\sin\left(2x-\frac{2\pi}{3}\right)$ ?

Period $=\frac{2\pi}{b}$

a)

$2\pi$

b)

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

c)

$\pi$

d)

$\frac{\pi}{3}$

48.

What is the maximum of the function $y=3\sin\left(2x-\frac{2\pi}{3}\right)$ ?

Max. $=\left|a\right|$

(a)

49.

What is the minimum of the function $y=3\sin\left(2x-\frac{2\pi}{3}\right)$ ?

Min. $=-\left|a\right|$

(a)

50.

Use the unit circle to match the angle measure: $\sin\pi$

a)

undefined

b)

$-1$

c)

$1$

d)

$0$

51.

What is the phase shift (horizontal shift) of the function $y=3\sin\left(2x-\frac{2\pi}{3}\right)$ ?

Phase Shift $=\frac{c}{b}$

a)

$\frac{\pi}{3}\$ units to the left

b)

$\frac{\pi}{3}$ units to the right

52.

Use a calculator to find to the degrees to the nearest hundredth of the expression $Sin^{-1}\left(0.87\right)=$ (a) . (Do not enter any words in your answer.)

53.

Use a calculator to find the degrees to the nearest hundredth of the expression $Cos^{-1}\left(-\frac{3}{5}\right)=$ (a) . (Do not enter any words in your answer.)

54.

Simplify the trig expression.

a)

sinx

b)

cosx

c)

cotx

d)

tanx

55.

Use the unit circle to match the angle measure: $\cos\left(\frac{7\pi}{4}\right)$

a)

$\frac{\sqrt[]{2}}{2}$

b)

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

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

56.

What is the phase shift (horizontal shift) of the function $y=\cos\left(2x-14\pi\right)$ ?

a)

$\pi$ units to the right

b)

$7\pi$ units to the right

c)

$14\pi$ units to the right

d)

$14\pi$ units to the left

57.

Which graph represents the function $f\left(x\right)=-2\cos x+1$ ?

a)

b)

c)

d)

58.

Check all that apply to $H\left(x\right)=Cos\left(x\right)$

a)

$Cos\left(x\right)$ has a restricted domain: $-\frac{\pi}{2}\le x\le\frac{\pi}{2}$

b)

$Cos^{-1}\left(x\right)$ exists

c)

its range is $\left[-1,1\right]$

d)

$Cos\left(\frac{3\pi}{4}\right)=-\frac{\sqrt{2}}{2}$

e)

The domain is restricted to QI and QII on the unit circle.

59.

$H^{-1}\left(x\right)=Cos^{-1}\left(x\right)$

a)

The domain is $\left[-1,1\right]$

b)

The range is $0\le x\le\pi$

c)

$Cos^{-1}\left(0\right)=\pi$

d)

$Cos^{-1}\left(-\frac{\sqrt{3}}{2}\right)=\frac{5\pi}{6}$

e)

$Cos^{-1}\left(\frac{\sqrt{3}}{2}\right)=\frac{\pi}{6}$

60.

Check all that apply to $G\left(x\right)=Sin\left(x\right)$

a)

$Sin\left(x\right)$ has a restricted domain: $-\frac{\pi}{2}\le x\le\frac{\pi}{2}$

b)

$Sin^{-1}\left(x\right)$ exists

c)

its range is $\left[-1,1\right]$

d)

$Sin\left(\frac{\pi}{4}\right)=1$

e)

The domain is restricted to QI and QII on the unit circle.

61.

$G^{-1}\left(x\right)=Sin^{-1}\left(x\right)$

a)

The domain is $\left(-\infty,\propto\right)$

b)

The range is $-\frac{\pi}{2}<x<\frac{\pi}{2}$

c)

$Sin^{-1}\left(\frac{\sqrt{2}}{2}\right)=\frac{\pi}{4}$

d)

$Sin^{-1}\left(-\frac{\sqrt{3}}{2}\right)=-\frac{\pi}{3}$

e)

$Sin^{-1}\left(0\right)=0$

62.

Check all that apply to $F\left(x\right)=Tan\left(x\right)$

a)

$Tan\left(x\right)$ has a restricted domain: $-\frac{\pi}{2}<x<\frac{\pi}{2}$

b)

$Tan^{-1}\left(x\right)$ exists

c)

its range is $\left[-1,1\right]$

d)

$Tan\left(-\frac{\pi}{4}\right)=-1$

e)

The domain is restricted to QI and QIV on the unit circle.

63.

$F^{-1}\left(x\right)=Tan^{-1}\left(x\right)$

a)

The domain is $\left(-\infty,\propto\right)$

b)

The range is $-\frac{\pi}{2}<x<\frac{\pi}{2}$

c)

$Tan^{-1}\left(1\right)=\frac{\pi}{4}$

d)

$Tan^{-1}\left(\sqrt{3}\right)=\frac{\pi}{3}$

e)

$Tan^{-1}\left(-\frac{\sqrt{3}}{3}\right)=-\frac{\pi}{6}$

64.

What is csc(x) equivalent to?

a)

$\frac{1}{\sin x}$

b)

$\frac{1}{\tan x}$

c)

sin(x)

d)

$\frac{1}{\cos x}$

65.

Simplify.

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

66.

Simplify.
cos²x + sin ²x=

a)

1

b)

csc²x + sec²x

c)

sin²x

d)

1 - sin²x

67.

a)

sinθ

b)

cot²θ

c)

tan²θ

d)

cos²θ

68.

Simplify the trig expression.

a)

1

b)

-tanx

c)

-1

d)

tanx

69.

Simplify

a)

csc x

b)

sec x

c)

cot x

d)

tan x

70.

Simplify

a)

-1

b)

sin θ

c)

csc θ

d)

1

71.

Simplify

a)

secθ

b)

cos²θ

c)

sin²θ

d)

$\frac{\sin^2x}{\cos^2x}$

72.

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

73.

Simplify.

a)

sinθ

b)

cos²θ

c)

sin²θ

d)

1- sin²θ

74.

Simplify.

a)

sin x

b)

cos x

c)

tan x

d)

1

75.

Simplify $\left(\csc x+1\right)\left(\csc x-1\right)$

a)

$\csc^2x+1$

b)

$\tan^2x$

c)

$\cot^2x$

d)

$2\csc x$

76.

a)

sec(u)

b)

cos(u)

c)

csc(u)

d)

sin(u)

e)

cot(u)

77.

a)

csc(u)

b)

cos(u)

c)

tan(u)

d)

sin(u)

e)

cot(u)

78.

a)

sec(u)

b)

cos(u)

c)

tan(u)

d)

sin(u)

e)

csc(u)

79.

Simplify: $\left(\cos\ θ\right)\left(\sec\ θ-\cosθ\right)$

a)

$\sin^2θ$

b)

$\cos^2θ$

c)

$\csc^2\theta$

d)

$\sec^2\theta$

80.

Simplify: $\sec x-\tan x\sin x$

a)

$\sin x$

b)

$\cos x$

c)

$\csc x$

d)

$\sec x$

81.

Simplify: $\frac{1-\sin^2x}{\sec x}$

a)

$\sin^2x$

b)

$\cos^2x$

c)

$\sin^3x$

d)

$\cos^3x$

82.

Simplify: $\frac{\cos^2\left(-x\right)\csc x}{\cot x}$

a)

$-\sin x$

b)

$-\cos x$

c)

$\sin x$

d)

$\cos x$

83.

$\cos\left(-\theta\right)=$

a)

$-\cos\left(\theta\right)$

b)

$\cos\left(\theta\right)$

c)

$-\cos\left(-\theta\right)$

84.

$\sin\left(-\theta\right)=$

a)

$-\sin\left(\theta\right)$

b)

$\sin\left(\theta\right)$

c)

$-\sin\left(-\theta\right)$

85.

$\tan\left(-\theta\right)=$

a)

$-\tan\left(\theta\right)$

b)

$\tan\left(\theta\right)$

c)

$-\tan\left(-\theta\right)$

86.

Evaluate:

\cos\left(2\pi\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

87.

Evaluate:

\tan\left(2\pi\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

88.

Evaluate:

\sin\left(\frac{3\pi}{4}\right)

a)

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

b)

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

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

89.

Evaluate:

\cos\left(\frac{5\pi}{3}\right)

a)

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

b)

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

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

90.

Evaluate:

\cos\left(\frac{5\pi}{4}\right)

a)

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

b)

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

c)

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

d)

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

91.

Evaluate:

\cos\left(\frac{7\pi}{6}\right)

a)

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

b)

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

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

92.

Evaluate:

\sin\left(2\pi\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

93.

Evaluate:

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

a)

$\sqrt{3}$

b)

$-\sqrt{3}$

c)

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

d)

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

94.

Evaluate:

\cos\left(\frac{3\pi}{2}\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

95.

Evaluate:

\sin\left(\frac{\pi}{2}\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

96.

Evaluate:

\cos\left(\frac{\pi}{4}\right)

a)

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

b)

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

c)

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

d)

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

97.

Evaluate:

\tan\left(\pi\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

98.

Evaluate:

\sin\left(\pi\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

99.

Evaluate:

\cos\left(\frac{\pi}{2}\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

100.

Evaluate:

\tan\left(\frac{\pi}{4}\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

101.

Evaluate:

\sin\left(\frac{4\pi}{3}\right)

a)

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

b)

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

c)

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

d)

$-\frac{1}{2}$

102.

Evaluate:

\cos\left(\frac{\pi}{6}\right)

a)

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

b)

$\frac{1}{2}$

c)

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

d)

$-\frac{1}{2}$

103.

Evaluate:

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

a)

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

b)

$\frac{1}{2}$

c)

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

d)

$-\frac{1}{2}$

104.

Evaluate:

\sin\left(\frac{7\pi}{6}\right)

a)

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

b)

$\frac{1}{2}$

c)

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

d)

$-\frac{1}{2}$

105.

Evaluate:

\tan\left(\frac{\pi}{2}\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

106.

Evaluate:

\cos\left(\pi\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

107.

Evaluate:

\tan\left(\frac{11\pi}{6}\right)

a)

$\sqrt{3}$

b)

$-\sqrt{3}$

c)

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

d)

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

108.

Evaluate:

\tan\left(\frac{7\pi}{4}\right)

a)

$1$

b)

$0$

c)

$-1$

d)

Undefined

109.

Evaluate:

\sin\left(\frac{\pi}{6}\right)

a)

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

b)

$\frac{1}{2}$

c)

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

d)

$-\frac{1}{2}$

110.

Evaluate:

\sin\left(\frac{7\pi}{4}\right)

a)

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

b)

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

c)

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

d)

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

111.

Solve over the interval $\left[-\frac{\pi}{2},\ \frac{\pi}{2}\right]$ : $\csc^2\ x+2\csc x\ -8=\ 0$

a)

$0.253,\ 2.889,\ \frac{7\pi}{6},\ \frac{11\pi}{6}$

b)

$-0.253,\ \frac{\pi}{6}$

c)

$3.394,\ 6.031,\ \frac{7\pi}{6},\ \frac{11\pi}{6}$

d)

$3.394,\ 6.031,\ \frac{\pi}{6},\ \frac{5\pi}{6}$

112.

Solve over the interval $\left[0,\ 2\pi\right)$ : $3\ \cos^{2\ }x\ +\ \cos\ x-1\ =\ 0$
Check ALL correct answers.

a)

$1.12,\ 5.16$

b)

$0.43,\ 5.85$

c)

$0.77,\ 2.44$

d)

$2.44,\ 3.84$

e)

$2.02,\ 5.16$

113.

Find the general solution of the equation.

a)

π/3; 2π/3

b)

π/6; 11π/6

114.

Solve the following equation over the interval $\left[0,\ 2\pi\right):$

$\tan^2\theta\ -\ 3\tan\theta\ +\ 2\ =\ 0$

Check ALL correct answers.

a)

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

b)

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

c)

$1.11,4.25$

d)

$2.03,5.17$

e)

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

115.

$5\cos^{2\ }x\ +\ 3\cos\ x\ =0$

Find all solutions to over the interval $\left[\frac{\pi}{2},\ \frac{3\pi}{2}\right)$

a)

0.927

b)

2.215

c)

4.069

d)

$\frac{\pi}{2}$

e)

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

116.

Solve sinθ = -1 on θ∈[0, 2π)

a)

θ = π /2, 3π /2

b)

θ = π /2

c)

θ = 3π /2

d)

θ = π

117.

Solve tanθ+1=2 on θ∈[0, 2π)

a)

0 and π

b)

3π/4 and 7π/4

c)

π/4 and 5π/4

d)

3π/4 and 5π/4

118.

Solve cosθ = -1 on [0, 2π)

a)

θ = π /2, 3π /2

b)

θ = π /2

c)

θ = 3π /2

d)

θ = π

119.

Solve\ \ \ 4\cos x+3=5\ \ \ for\ 0\le x<360\degree

a)

$x\ =\ 60\degree,\ 120\degree$

b)

$x\ =\ 60\degree,\ 300\degree$

c)

$x\ =\ 30\degree,\ 150\degree$

d)

$x\ =\ 30\degree,\ 330\degree$

120.

Why doesn't 2cosx − 3 = 0 have solutions?

a)

cos x is never bigger than one

b)

cos x is never equal to a fraction

c)

Actually, this equation does have a solution, x = π

d)

This equation will have a solution tomorrow.

121.

Solve equation for $0\le\theta<2\pi$ .
$3\sin^2\theta=7\sin^2\theta+4\sin\theta+1$

a)

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

b)

$\theta=0,\frac{\pi}{3},\frac{5\pi}{3}$

c)

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

d)

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

122.

Solve on the domain [0, 2π)
cos² x + sin x + 1 = 0

a)

π

b)

3π/2

c)

π/6, 5π/6, 3π/2

d)

No solution

123.

Solve over the interval $\left[0,2\pi\right)$

$3\sin\theta=\sqrt[]{3}\cos\theta$

a)

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

b)

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

c)

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

d)

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

124.

Solve the equation over the interval [ $\frac{\pi}{2},\pi$ ]

$\frac{2\tan\theta}{3-\tan^2\theta}=1$

Type in your answer rounded to the nearest thousandths (3 decimals).

(a)

125.

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

a)

π/3; 5π/3

b)

no solution

c)

π/6; 5π/6

126.

Solve the equation over the interval [ $\frac{\pi}{2},\pi$ ]

$\frac{2\tan\theta}{3-\tan^2\theta}=1$

Type in your answer rounded to the nearest tenth

(a)

127.

Solve:

2\cos2x+3=2

a)

$x=\frac{2\pi}{3}+2n\pi;\ x=\frac{4\pi}{3}+2n\pi$

b)

$x=\frac{\pi}{3};\ x=\frac{2\pi}{3}$

c)

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

d)

$x=-\frac{1}{4}$

128.

Solve in the interval [0, 2π):

2\sin3x-1=0

a)

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

b)

$x=\frac{\pi}{18};\ x=\frac{5\pi}{18}$

c)

$x=\frac{\pi}{9};\ x=\frac{2\pi}{9}$

d)

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

129.

Choose the correct ratio.

a)

sin(37)=x/14

b)

cos(37)=x/14

c)

tan(37)=x/14

d)

sin(37)=14/x

130.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

131.

Which trigonometric ratio should you use?

a)

Tangent Ratio

b)

Sine Ratio

c)

Cosine Ratio

d)

Any ratio

132.

What is the amplitude of this function?

a)

2

b)

2π

c)

-2

d)

1

133.

Sine or Cosine?

a)

y=sinx

b)

y=cosx

134.

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

135.

Find the measure of the missing angle.

a)

64^o

b)

26^o

c)

61^o

d)

.008^o

136.

Solve for x. Round to the nearest tenth.

a)

7.5

b)

34.1

c)

14.1

10054 Unit 3 Review (Topics 18-23): Trigonometry

Total questions: 136

Worksheet time: 2hrs 19mins

Similar Resources on Wayground