Free Printable Unit 6 Review Precalc

1.

What is 5π/6 radians in degrees?

a)

180

b)

150

c)

360

d)

120

2.

What is 7π/4 radians in degrees?

a)

300

b)

135

c)

315

d)

45

3.

What is 2π/3 radians in degrees?

a)

150

b)

120

c)

180

d)

30

4.

What character is this?

a)

Pocahontas

b)

Moana

c)

Cinderella

d)

Merida

5.

What is π/3 radians in degrees?

a)

30

b)

60

c)

360

d)

90

6.

Which of the following is closest to the measure of the angle shown?

a)

7/10 π

b)

3/8 π

c)

7/20 π

d)

3/2 π

7.

Which of the following is closest to the measure of the angle drawn by the green curve?

a)

5/6 π

b)

5/3 π

c)

4/5 π

d)

4/3 π

8.

How many radians does a circle have?

a)

360 degrees

b)

2pi radians

c)

pi radians

d)

^{2 radians}

9.

What is 360 degrees in radians?

a)

2π/3

b)

5π/4

c)

2π

d)

π

10.

How many radians are there in half a circle?

a)

2 pi

b)

180^o

c)

360^o

d)

pi

11.

Convert 100⁰ to radians

a)

5π/9

b)

π/2

c)

5π/8

d)

5π/6

12.

Convert the following to radians:
720⁰

a)

3π

b)

4π

c)

5π

13.

Convert the following to degrees:
-8π/5 radians

a)

-288⁰

b)

-260⁰

c)

-275⁰

14.

What are the negative and positive coterminal angles of -225 degrees?

a)

375°, -600°

b)

125°, -356°

c)

135°, -585°

d)

60°, -120°

15.

$\frac{8\pi}{3}$ is equivalent to what degree measure?

a)

$480\degree$

b)

$240\degree$

c)

$800\degree$

d)

$24\degree$

16.

Which of the following angles are co-terminal to 330^o?

a)

-330^o, 330^o

b)

510^o, -210^o

c)

690^o, -30^o

d)

420^o, -330^o

17.

Which of the following angles are co-terminal to -75^o?

a)

-365^o, 75^o

b)

285^o, -435^o

c)

105^o, -255^o

d)

425^o, -335^o

18.

In which quadrant is -570⁰

a)

I

b)

II

c)

III

d)

IV

19.

In which quadrant would you find an angle measuring -700°?

a)

1

b)

2

c)

3

d)

4

20.

Which is a coterminal angle to the angle shown?

a)

613

b)

73

c)

-117

d)

17

21.

What is the value of sine at 30

a)

1/2

b)

√3 / 2

c)

0

d)

√2 ⁄ 2

22.

sin π/4

a)

√2∕2

b)

1/2

c)

√3/2

d)

0

23.

sec 3π/2

a)

0

b)

undefined

c)

1

d)

-1

24.

cos 5π/6

a)

-1/2

b)

1/2

c)

√3/2

d)

-√3/2

25.

tan 7π/4

a)

-1

b)

1

c)

√2/2

d)

undefined

26.

cos 4π/3

a)

-√3/2

b)

√3/2

c)

1/2

d)

-1/2

27.

cot 3π/4

a)

-√2/2

b)

-1

c)

1

d)

√2/2

28.

sin 7π/6

a)

1/2

b)

-1/2

c)

√3/2

d)

-√3/2

29.

tan (-π)

a)

undefined

b)

0

c)

1

d)

-1

30.

sin x =

a)

cos x

b)

1/cosx

c)

1/secx

d)

1/cscx

31.

cos x =

a)

sin x

b)

sin²x-1

c)

1/sec x

d)

1/csc x

32.

tan x =

a)

sinx/cos x

b)

cosx/sinx

c)

1/cotx

d)

sec²x

33.

sec x =

a)

1/cosx

b)

1/sinx

c)

1/cscx

d)

1/tanx

34.

csc x =

a)

1/cosx

b)

1/sinx

c)

cot²x-1

d)

1/secx

35.

cotx =

a)

sinx/cosx

b)

cosx/sinx

c)

1/tanx

d)

1/cotx

36.

sin²x + cos²x =

a)

1

b)

1/sinx

c)

sec²x

d)

csc²x

37.

1 - sin²x =

a)

cos²x

b)

cos²x+1

c)

csc²x

d)

tan²x

38.

tan²x + 1 =

a)

csc²x

b)

sec²x

c)

sec²x - 1

d)

cscx

39.

1 + cot²x =

a)

sec²x

b)

sec²x - 1

c)

tan²x

d)

csc²x

40.

1 - cos²x =

a)

sec²x

b)

csc²x

c)

sin²x

d)

sec²x - 1

41.

sec²x =

a)

sinx + cosx

b)

1 + csc²x

c)

1 + tan²x

d)

1 - sin²x

42.

csc²x - 1 =

a)

cot²x

b)

tan²x

c)

cot²x + 1

d)

sin²x + cos²x

43.

sec²x - 1 =

a)

cot²x

b)

csc²x

c)

1 + tan²x

d)

tan²x

44.

1/cosx =

a)

secx

b)

cscx

c)

tanx

d)

sinx

45.

1/tanx =

a)

tanx

b)

sinx/cosx

c)

cotx

d)

sin²x

46.

cos²x =

a)

1 - sec²x

b)

1 - sin²x

c)

sin²x

d)

1

47.

Which of these is equivalent to 2cos²x − 3cosx = 0 ?

a)

-cos²x = 0

b)

cosx(2cosx + 3) = 0

c)

cosx(2cosx − 3) = 0

d)

cos x = ⅔

48.

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

a)

cosx is never bigger than one

b)

cosx is never equal to a fraction

c)

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

d)

This equation will have a solution tomorrow.

49.

Choose a good way to start solving this equation

tanx sin²x = 2 tanx

a)

divide tanx from both sides

b)

factor out tanx

c)

subtract 2 tanx from the left and then factor tanx out

d)

cancel sin²x out

50.

On the domain [0, 2π), solve this equation 0 = sinx(sinx − 1)

a)

0, π

b)

0, π, ½π

c)

½π

d)

0, 90, 270

51.

csc²x = 2 is equivalent to sin²x = ½

a)

True

b)

False

52.

Factor: sec²x − secx − 2

a)

(sec x)(secx − 2)

b)

(secx − 2)(secx − 1)

c)

(secx − 2)(secx + 1)

d)

(secx + 2)(secx − 1)

53.

Solve the following for tan²θ:
1 + tan²θ = sec²θ

a)

tan²θ = sec²θ + 1

b)

tan²θ = sec²θ - 1

c)

tanθ = secθ - 1

d)

tan²θ = opp/adj

54.

Which of these is equivalent to 2cos²x − 3cosx = 0 ?

a)

-cos²x = 0

b)

cosx(2cosx + 3) = 0

c)

cosx(2cosx − 3) = 0

d)

cos x = ⅔

e)

I have no idea

55.

On the interval [0, 2π), solve this equation 0 = sinx(sinx − 1)

a)

0, π

b)

0, π, ½π

c)

½π

d)

0^o, 90^o, 270^o

e)

I have no idea

56.

Simplify sec²(x) - tan²(x)

a)

tan(x)

b)

1

c)

-sin(x)

d)

-1

e)

I have no idea

57.

Simplify (sec²x)(1 - sin²x)

a)

-cos(x)

b)

1

c)

-1

d)

-sin(x)

e)

I have no idea

58.

Simplify sin²(x) - cos(x)sec(x)

a)

sec²(x)

b)

cos²(x)

c)

-cos²(x)

d)

-sec²(x)

e)

I have no idea

59.

Simplify 1 + tan²(β)

a)

cos²(β)

b)

-cos²(β)

c)

-sec²(β)

d)

sec²(β)

e)

I have no idea

60.

Simplify sinx cot x

a)

sinx

b)

cosx

c)

tanx

d)

cotx

e)

I have no idea

61.

sin2u =

a)

(sinu)(cosu)

b)

2(sinu)(cosu)

c)

(sinu)²

d)

2(sinu)²

e)

I have no idea

62.

cos2u =

a)

2(sinu)(cosu)

b)

(cosu)² - (sinu)²

c)

2(cosu)² - 2

d)

(sinu)² - (cosu)²

e)

I have no idea

63.

Which of these are equal to 1? (Check all that apply)

a)

sin²(θ) + cos²(θ)

b)

sec²(θ) - tan²(θ)

c)

csc²(θ) - cot²(θ)

d)

tan²(θ) - cos²(θ)

64.

Which of these is false?

a)

$\cos\left(\frac{\pi}{2}-\theta\right)=\sin\left(\theta\right)$

b)

$\sin\left(\frac{\pi}{2}-\theta\right)=\cos\left(\theta\right)$

c)

$\sec\left(\frac{\pi}{2}-\theta\right)=\cos\left(\theta\right)$

d)

$\tan\left(\frac{\pi}{2}-\theta\right)=\cot\left(\theta\right)$

65.

Which of these is false?

a)

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

b)

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

c)

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

66.

Each trig function has a "cofunction" (Ex: sine and cosine are cofunctions).

How are cofunctions related to each other? (Check all that apply)

a)

Cofunctions of complementary angles are equal.

b)

Cofunctions are reciprocals of each other.

c)

Cofunctions are inverses of each other.

d)

Cofunctions are negatives of each other.

67.

$\frac{\tan\left(\theta\right)}{\cot\left(\theta\right)}\equiv$

a)

$1$

b)

$\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

c)

$\tan^2\left(\theta\right)$

d)

$\sec^2\left(\theta\right)$

68.

Solve for x:
$2\cos^2\left(x\right)+\cos\left(x\right)-1=0$
Check all possible answers

a)

x = 0

b)

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

c)

x = $\pi$

d)

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

e)

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

69.

Solve for x:
$\tan\left(x\right)-\tan\left(x\right)\tan^2\left(\frac{\pi}{12}\right)\ =\ 2\tan\left(\frac{\pi}{12}\right)$

a)

x = $\frac{\pi}{12}$

b)

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

c)

x = $0$

d)

x = $\pi$

70.

Which of the following is equivalent to $\sin\left(\alpha+\beta\right)$ ?

a)

$\sin\alpha\cos\alpha+\sin\beta\cos\beta$

b)

$\sin\alpha\cos\alpha-\sin\beta\cos\beta$

c)

$\sin\alpha\cos\beta+\cos\alpha\sin\beta$

d)

$\sin\alpha\cos\beta-\cos\alpha\sin\beta$

71.

Which of the following is equivalent to $\cos\left(\alpha-\beta\right)$ ?

a)

$\cos\alpha\cos\beta+\sin\alpha\sin\beta$

b)

$\cos\alpha\cos\beta-\sin\alpha\sin B$

c)

$\cos\alpha\sin\beta+\sin\alpha\cos\beta$

d)

$\cos\alpha\sin\beta-\sin\alpha\cos\beta$

72.

Which of the following is equivalent to $\tan\left(\alpha+\beta\right)$ ?

a)

$\frac{\tan\alpha+\tan\beta}{1-\tan\alpha\tan\beta}$

b)

$\frac{\tan\alpha-\tan\beta}{1-\tan\alpha\tan\beta}$

c)

$\frac{\tan\alpha+\tan\beta}{1+\tan\alpha\tan\beta}$

d)

$\frac{\tan\alpha-\tan\beta}{1+\tan\alpha\tan\beta}$

73.

Find the exact value of $\sin105\degree$

a)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

b)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

c)

$\frac{\sqrt{6}+\sqrt{2}}{4}$

d)

$\frac{\sqrt{3}+1}{2}$

74.

$\cos105\degree$

a)

$\frac{\sqrt{2}+\sqrt{6}}{4}$

b)

$\frac{\sqrt{2}-\sqrt{6}}{4}$

c)

$\frac{\sqrt{6}-\sqrt{2}}{4}$

d)

$\frac{1-\sqrt{3}}{2}$

75.

If $\sin\alpha=\frac{5}{13}$ and $\cos\beta=\frac{4}{5}$ (both in QI), find $\cos\left(\alpha+\beta\right)$

a)

$\frac{33}{65}$

b)

$-\frac{33}{65}$

c)

$\frac{63}{65}$

d)

$-\frac{63}{65}$

76.

cos(2x) is NOT equal to which of the following?

a)

1 - sin²x

b)

2cos²x - 1

c)

1 - 2sin²x

d)

cos²x - sin²x

77.

$\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$

Use the Addition & Subtraction Identities to simplify the expression above.

a)

$\sin\ 90^{o\ }$

b)

$\sin\ 60^{o\ }$

c)

$\cos\ 90^{o\ }$

d)

$\cos\ 60^{o\ }$

78.

Use the Addition & Subtraction Identities to solve $\cos\ \left(90^o-x\right)$

a)

$\cos\ x$

b)

$\sin\ x$

c)

$\tan\ x$

d)

$-\cos x$

79.

Use the Sum to Product Identities to rewrite the following expression: $\cos129\degree+\cos45\degree$

a)

$-2\cos87\degree\cos42\degree$

b)

$-2\sin87\degree\sin42\degree$

c)

$-2\sin87\degree\cos42\degree$

d)

$2\cos87\degree\cos42\degree$

80.

What's the capital of Spain?

a)

Malaga

b)

Alicante

c)

Madrid

d)

Barcelona

81.

What's the capital of Portugal?

a)

Porto

b)

Lisbon

c)

Dublin

d)

Coimbra

82.

What movie is this ?

a)

Black Beauty

b)

Little Mermaid

c)

Beauty and The Beast

d)

Rapunzel

83.

What are the names of the two princess sisters?

a)

Mulan and Snow white

b)

Helga and Mulan

c)

Anna and Dana

d)

Anna and Elsa

84.

a)

Highlander

b)

Hyundai

c)

Honda

d)

Hillman

85.

a)

Party French

b)

Pepsi

c)

Cocoa Cola

d)

Coke

Unit 6 Review Precalc

Total questions: 85

Worksheet time: 2hrs 52mins

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