Free Printable Trigonometry Final Exam Review 2022

1.

What is the period of the following function?

a)

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

b)

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

c)

$2\pi$

d)

3

2.

What is the b-value of the following function? y=acosb(x+c)+d

a)

1

b)

2

c)

3

d)

4

3.

Match the following equations with the graph given.

a)

$y=-3\sin\left(x\right)-4$

b)

$y=3\sin\left(x\right)-4$

c)

$y=3\cos\left(x\right)-4$

d)

$y=-3\cos\left(x\right)-4$

4.

The __________ represents half the distance between the max and min of a sine or cosine graph.

a)

Period

b)

Frequency

c)

Extreme Values

d)

Amplitude

5.

The period of a sine or cosine graph can be found by the following formula:

a)

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

b)

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

c)

$2\pi b$

d)

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

6.

What is the midline for the following equation:

$y=2\cos\left(\frac{1}{3}x+\frac{\pi}{6}\right)+2$

a)

1/3

b)

-2

c)

+2

d)

4

7.

Write the equation for a sine function with an amplitude of 6, a period of π/4 and a downward vertical translation of 4.

a)

y=6 sin (8x) - 4

b)

y=6 sin 8(x-1) - 4

c)

y=6 sin (π/4) + 4

d)

y=6 sin (π/4 x) + 4

8.

What is the radius of the unit circle?

a)

1.5

b)

2

c)

1/2

d)

1

9.

The value of sinθ is positive in

a)

the 1st and 2nd quadrants

b)

the 1st and 3rd quadrants

c)

the 1st and 4th quadrants

d)

the 2nd and 3rd quadrants

10.

What is the sin 45°?

a)

1

b)

^√3/₂

c)

½

d)

^√2/₂

11.

If the tangent ratio of a right triangle is $\frac{48}{14}$ what is the cosine ratio?

a)

$\frac{14}{50}$

b)

$\frac{48}{50}$

c)

$\frac{14}{48}$

d)

$\frac{50}{14}$

12.

The value of cos(-240⁰) is

a)

0.5

b)

-0.5

c)

-0.866

d)

-0.707

13.

The terminal side of a 330° angle is in what Quadrant?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

14.

Graph the angle in standard position. $-220\degree$

a)

b)

c)

d)

15.

Positive angles are measured in which direction from standard position?

a)

Clockwise

b)

Counterclockwise

16.

What is the reference angle for 315°?

a)

30

b)

45

c)

60

d)

90

17.

What are the coordinates of 60° on the unit circle?

a)

(0, 1)

b)

(1/2, √3/2)

c)

(√3/2, 1/2)

d)

(√2/2, 1/2)

18.

What is the exact value of sin 150°

a)

-1/2

b)

-√3/2

c)

1/2

d)

√3/2

19.

What are the coordinates of 210° on the unit circle?

a)

(−√3/2, −1/2)

b)

(√3/2, −1/2)

c)

(−√3/2, 1/2)

d)

(−1/2,−√3/2 )

20.

Which trig function does this graph represent?

a)

sin

b)

sec

c)

tan

d)

cot

21.

Which function below matches this graph?

a)

2+sec(x)

b)

sec2(x)

c)

2sec(x)

d)

sec(x-2)

22.

Write an equation or the graph.

a)

y = 2sec(x)

b)

y = 3sec(x)

c)

y = 3sec(2x)

d)

y = 3csc(x)

e)

y = 3csc(2x)

23.

What is the period of this function?

a)

\frac{\pi}{4}

b)

$\frac{\pi}{2}$

c)

$\pi$

d)

$2\pi$

24.

A trig function has an amplitude of 4 and a minimum value of 5. What is its maximum value?

a)

7

b)

9

c)

11

d)

13

25.

What trigonometric functions have vertical asymptotes? Select all that apply.

a)

sine

b)

cosine

c)

tangent

d)

secant

e)

cosecant

26.

Which of the following is an asymptote for secant?

a)

x= π

b)

x = 3π / 2

c)

x = -2π

d)

x = 0

27.

If $\sec\theta>0$ and $\sin\theta<0$ then $\theta$ must be in which quadrant?

a)

I

b)

II

c)

III

d)

IV

28.

Simplify to a single term: $\sec\left(x\right)\cos\left(x\right)$

4 lines

29.

Simplify to a single term: $\tan^2\left(x\right)-\sec^2\left(x\right)$

a)

$\cot^2\left(x\right)$

b)

-1

c)

$\sin^2\left(x\right)$

d)

1

30.

Simplify to a single term: $\frac{\sec^2\left(x\right)-1}{\sin^2\left(x\right)}$

a)

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

b)

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

c)

$\csc^2\left(x\right)$

d)

$\frac{1}{\sin^2\left(x\right)}$

31.

Factor and Simplify: $\tan^2\left(x\right)-\tan^2\left(x\right)\sin^2\left(x\right)$

a)

$\cos^2\left(x\right)$

b)

$\tan^2\left(x\right)\left(1-\sin^2\left(x\right)\right)$

c)

$\tan^2\left(x\right)\left(\sin^2\left(x\right)-1\right)$

d)

$\sin^2\left(x\right)$

32.

Factor and Simplify: $\tan^4\left(x\right)+2\tan^2\left(x\right)+1$

a)

$\left(\tan\left(x\right)+1\right)^2$

b)

$\sec\left(x\right)$

c)

$\left(\tan^2\left(x\right)+1\right)^2$

d)

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

33.

Factor and Simplify: $\sin^4\left(x\right)-\cos^4\left(x\right)$

a)

$\sin^2\left(x\right)+\cos^2\left(x\right)$

b)

1

c)

$\sin^2\left(x\right)-\cos^2\left(x\right)$

d)

-1

34.

Simplify: $\frac{1}{1+\cos\left(x\right)}+\frac{1}{1-\cos\left(x\right)}$

a)

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

b)

$2\sin^2\left(x\right)$

c)

$2\cos^2\left(x\right)$

d)

$2\csc^2\left(x\right)$

35.

Simplify: $\frac{\cos\left(x\right)}{1+\sin\left(x\right)}+\frac{1+\sin\left(x\right)}{\cos\left(x\right)}$

a)

$2\cos\left(x\right)$

b)

$2\sec\left(x\right)$

c)

$2\sin\left(x\right)$

d)

$2\csc\left(x\right)$

36.

Simplify:

\left(\sin\left(x\right)+\cos\left(x\right)\right)^2

a)

$\sin^2\left(x\right)+\cos^2\left(x\right)$

b)

$1$

c)

$1+2\sin\left(x\right)\cos\left(x\right)$

d)

$\sin^2\left(x\right)+2\sin\left(x\right)\cos\left(x\right)+\cos^2\left(x\right)$

37.

Cos^-1(√3/2) =

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

38.

Sin^-1[cosπ]

a)

0

b)

π

c)

π/2

d)

-π/2

39.

Cos^-1(0) =

a)

½π

b)

π

c)

1

d)

none of these

40.

What range of angles can you get from the principal value of inverse cosine?

a)

0 to π

b)

0 to 2π

c)

-π/2 to π/2

d)

π/2 to 3 π/2

41.

Arctan (0)

a)

1

b)

0

c)

-1

d)

0.5

42.

Arcsin(cos π/6)

a)

π/6

b)

π/3

c)

-π/6

d)

π/4

43.

$\tan^{-1}\sqrt{3}-\sec^{-1}\left(-2\right)=$

a)

$\pi$

b)

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

c)

$\frac{\pi}{3}$

d)

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

44.

$\sin^{-1}\left[\cos\left(\sin^{-1}\left(\frac{\sqrt{3}}{2}\right)\right)\right]=$

a)

$\frac{\pi}{6}$

b)

$\frac{\pi}{3}$

c)

$\frac{\pi}{4}$

d)

$\frac{\pi}{2}$

45.

Inverse function of Sine of an angle ?

a)

Cosine

b)

Cosecant

c)

Secant

d)

Cotangent

46.

Sin^-1[cosπ]

a)

0

b)

π

c)

π/2

d)

-π/2

47.

$\tan^{-1}\sqrt{3}-\sec^{-1}\left(-2\right)=$

a)

$\pi$

b)

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

c)

$\frac{\pi}{3}$

d)

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

48.

a)

A

b)

B

c)

C

d)

D

49.

Solve for 0≤x≤2π

2cos²x + cosx = 0

a)

π/2, 3π/2

b)

0, π,2π

c)

2π/3, 4π/3

d)

π/3, 5π/3

50.

Solve for 0≤x≤2π

4cos²x- 2 = 0

a)

π/3, 5π/3

b)

π/4, 7π/4

c)

3π/4, 5π/4

d)

π/6, 11π/6

51.

Solve for 0≤x≤2π

2sin²x - 5sinx + 2 = 0

a)

π/6, 5π/6

b)

7π/6, 11π/6

c)

π/3, 2π/3

d)

4π/3, 5π/3

52.

Which of the following is NOT

a solution to

tan θ = 0 ?

a)

θ = 0

b)

θ = π /2

c)

θ = π

d)

θ = 2π

53.

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

a)

0

b)

No solution

c)

π

d)

3π/2

54.

Solve for x: $5\cos x+\sqrt{2}=3\cos x$

a)

$\pi$

b)

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

c)

DNE

d)

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

55.

Select all possible answers to the equation $4\sin^2u+8=11$

a)

$\frac{\pi}{3}$

b)

$2\pi$

c)

$\frac{\pi}{6}$

d)

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

e)

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

56.

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

a)

0, π, π/6, 5π/6,

b)

0, π/6, 7π/6

c)

π, 5π/6, 11π/6

d)

π, π/6, 5π/6, 7π/6, 11π/6

57.

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.

58.

sin2u =

a)

(sinu)(cosu)

b)

2(sinu)(cosu)

c)

(sinu)^2

d)

2(sinu)^2

59.

cos2u =

a)

2(sinu)(cosu)

b)

(cosu)^2 - (sinu)^2

c)

2(cosu)^2 - 2

d)

(sinu)^2 - (cosu)^2

60.

If cosx = - 4/5, find csc if in quadrant II

a)

1/2

b)

-3/5

c)

5/3

d)

√3/2

61.

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant.

a)

120/169

b)

25/169

c)

60/169

d)

5/13

62.

Using the second identity, find Cos(50)

a)

sin²(25) - cos²(25)

b)

cos²(50) - sin²(50)

c)

cos²(25) - sin²(25)

d)

sin²(50) - cos²(50)

63.

Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

64.

Use a double-angle or half-angle identity to find the exact value of each expression
sin θ = −3/5 and 3π/2 < θ < 2π Find tan θ/2

a)

-1/3

b)

-√3

c)

√3/3

d)

-1

65.

Use a double-angle identity to find the exact value of each expression
cos θ = 4/5 and 270° < θ < 360°
Find sin 2θ

a)

-1/5

b)

24/25

c)

-24/25

d)

-25/24

66.

Use the information about the angle θ, 0≤θ<2π to find the exact value of
sin (2θ)
1. sin θ= 3/5 , 0<θ<π/2

a)

24/7

b)

7/25

c)

24/25

d)

1/2

67.

Use Sum or Difference Identities to find the exact value of each expression.

cos(75°)

a)

1/4

b)

c)

d)

68.

Solve the following for cos²θ:
sin²θ + cos²θ = 1

a)

cos²θ = 1 - sin²θ

b)

cosθ = 1 + sin²θ

c)

cosθ = 1 - sinθ

d)

cos²θ = Adj/hyp

69.

Please select the correct solution

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

70.

Is this a pythagorean identity?
tan²x + 1 = secx

a)

Yes

b)

No

71.

If $\sin\theta=\frac{4}{5}$ , find $\csc\theta$ .

a)

$\frac{9}{5}$

b)

$\frac{5}{4}$

c)

$\frac{1}{5}$

d)

$\frac{1}{4}$

72.

Simplify (sec²x)(1 - sin²x)

a)

-cos(x)

b)

1

c)

-1

d)

-sin(x)

73.

Use Sum or Difference Identities to find the exact value of each expression.

cos(75°)

a)

1/4

b)

√6/4 - √2 / 4

c)

√6 + √2 / 4

d)

-√6/4 - √2 / 4

74.

Expand $\cos\ \left(\frac{\pi}{5}+\frac{\pi}{6}\right)$

a)

$\cos\frac{\pi}{5}\cos\frac{\pi}{6}-\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$

b)

$\cos\frac{\pi}{5}\cos\frac{\pi}{6}+\sin\frac{\pi}{5}\sin\frac{\pi}{6}\$

c)

$\cos\ \frac{2\pi}{11}$

d)

$\cos\frac{\pi}{5}\sin\frac{\pi}{6}-\cos\frac{\pi}{5}\sin\frac{\pi}{6}\$

75.

$\cos75^o\cos15^o-\sin75^{o\ }\sin15^o$ is equivalent to

a)

$\sin\ 90^{o\ }$

b)

$\sin\ 60^{o\ }$

c)

$\cos\ 90^{o\ }$

d)

$\cos\ 60^{o\ }$

76.

$\frac{\tan45^o+\tan30^o}{1-\tan45^o\tan30^o}$ is equivalent to

a)

$\tan75^o$

b)

$\tan\ 15^o$

c)

$\frac{\sin45^o}{\cos30^o}$

d)

$\tan90^{o\ }$

77.

Simplify the following expression.

a)

b)

c)

d)

Trigonometry Final Exam Review 2022

Total questions: 77

Worksheet time: 19hrs 15mins

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