Free Printable Graph of Trig Functions & Inverse Functions

1.

sin[arcsin( $\frac{1}{2}$ )]

a)

$\frac{\pi}{6}$

b)

$\frac{1}{2}$

c)

$60\degree$

d)

no solution

2.

arccos[cos( $\frac{7\pi}{4}$ )]

a)

$\frac{\pi}{4}$

b)

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

c)

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

d)

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

3.

tan[arctan(10)]

a)

no solution

b)

-10

c)

$\frac{1}{10}$

d)

10

4.

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)

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

5.

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

a)

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

b)

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

c)

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

d)

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

6.

cos^-1(0) =

a)

π/2

b)

π

c)

1

d)

none of these

7.

tan^-1(√(3))

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

8.

What is the range of the inverse sine function?

a)

[0, π]

b)

[0, 2π]

c)

[-π/2, π/2]

d)

[π/2, 3π/2]

9.

This is the equation of which graph?

a)

y= cot x

b)

y = tan x

c)

y = cot^-1 x

d)

y = tan^-1x

10.

y = arcsin x is the same graph as which of the following?

a)

y= csc x

b)

y = sec x

c)

y = sin^-1 x

d)

y = csc^-1x

11.

This is the equation of which graph?

a)

y = sin x

b)

y = cos x

c)

y = sec x

d)

y = csc x

12.

a)

-π/3

b)

4π/3

c)

-2π/3

d)

2π/3

13.

a)

0

b)

π/2

c)

2π

d)

3π

14.

a)

π/6

b)

5π/6

c)

7π/6

d)

2π

15.

a)

π/2

b)

π

c)

3π/2

d)

-3π/2

16.

Evaluate the function: arcsin(-1/2)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

17.

arccos (-√3/2)

a)

5π/6

b)

2π/3

c)

-π/6

d)

7π/6

18.

Evaluate the function: tan[sin^-1(-1/2)]

a)

√3

b)

√3/3

c)

-√3

d)

-√3/3

19.

cos^-1[tan(-π/4)] =

a)

0

b)

π

c)

π/4

d)

3π/4

20.

What is the RANGE of angles for inverse sine?

a)

[0, π]

b)

[-1, 1]

c)

[-π/2, π/2]

d)

(-∞, ∞)

21.

What RANGE of angles for inverse cosine?

a)

[0, π]

b)

(-∞, ∞)

c)

[-π/2, π/2]

d)

[-1, 1]

22.

What is the RANGE of angles for inverse tangent?

a)

[-π/4, π/4]

b)

(-π/2, π/2)

c)

[0, π]

d)

(-∞, ∞)

23.

What is the period
of
y = 3 sin 2x?

a)

2

b)

3

c)

180

d)

360

24.

What is the amplitude of y = 3 cos 2x?

a)

3

b)

2

c)

90
90⁰

d)

350⁰

25.

What is the period
of
y = 3 sin 2x?

a)

2

b)

3

c)

180

d)

360

26.

What is the amplitude of y = 3 cos 2x?

a)

3

b)

2

c)

90
90⁰

d)

350⁰

27.

What is the amplitude of this function?

a)

2

b)

2π

c)

-2

d)

1

28.

Determine the equation

a)

tan x

b)

cot x

c)

tan 2x

d)

cot 2x

29.

Write an equation of a sine function with a period of π and amplitude of 7.

a)

y=7sin2πx

b)

y=7sinπx

c)

y=2sin7x

d)

y=7sin2x

30.

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

a)

$\pi$

b)

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

c)

$\frac{\pi}{3}$

d)

$2\pi$

e)

$\frac{2}{3}$

31.

$2\sin\theta\cos\theta=2\ \$ find for $\left(\sin\theta-\cos\theta\right)^2=?$

a)

1

b)

0

c)

-1

d)

1

e)

-2

32.

What is the range of $y=-3\sin\left(4x+\pi\right)$

a)

$-3\le y\le3$

b)

$-2\le y\le4$

c)

$-1\le y\le-5$

d)

$0\le y\le2\pi$

e)

all real numbers

33.

$For\ \frac{\pi}{2}\le\theta\le\pi\ ,\ and\ \cos\theta=\frac{\sqrt[]{3}}{2}\ ,\ find\ \ 1+\frac{1}{\tan^2\theta}=?$

a)

1/4

b)

4

c)

1

d)

4/3

34.

$6\cos\left(x\right).6\cos\left(-x\right)+4.\sin\left(-x\right).-9\left(\sin\left(x\right)\right)$

a)

-36

b)

-72

c)

72

d)

36

e)

$36\left(\cos^2x-\sin^2x\right)$

35.

Simplify: $(\secθ-1)(\secθ+1)$

a)

sin ² θ

b)

cos ² θ

c)

tan ² θ

d)

sec ² θ

36.

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

a)

$\sin^2x$

b)

$\csc^2x$

c)

$\cos^2x$

d)

$\sec^2x$

37.

Simplify: $\frac{\sin^2x+\cos^2x+\cot^2x}{1+\tan^2x}$

a)

$\cot^2x$

b)

$\tan^2x$

c)

$\csc^2x$

d)

$\sec^2x$

38.

a)

csc²θ

b)

sec²θ

c)

cscθ

d)

1

39.

Simplify the trig expression.

a)

tan²x

b)

-tan²x

c)

cot²x

d)

cos²x*sin²x

40.

Simplify the trig expression.

a)

1

b)

-1

c)

cotx

d)

cosx

41.

$\cot^2x\sin^2x+\tan^2x\cos^2x$

a)

secx

b)

cosx

c)

tanx

d)

1

42.

$\sin x\left(\csc x-\sin x\right)$

a)

$\sec^2x$

b)

$\cos x$

c)

$\cos^2x$

d)

$\sin x\sec x$

43.

$\frac{\sin^2x}{1-\cos^2x}$

a)

$\sin^2x$

b)

1

c)

$\sin^4x$

d)

$\sin^2x-\tan^2x$

44.

What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

45.

Which of the following is the correct cosine equation for the given graph?

a)

y = - 6 cos x - 1

b)

y = 3 cos x - 4

c)

y = -7 cos x

d)

y = -3 cos x - 4

46.

Which of the following parent functions do NOT have a period of $2\pi$ ?

a)

y = sin x

b)

y = tan x

c)

y = csc x

47.

What is the domain and range of y=sinx?

a)

D: (-∞, ∞)
R: [-1, 1]

b)

D: (-∞, ∞)
R: [-π, π]

c)

D: (∞, -∞)
R: [-1, 1]

d)

D: (-∞, ∞)
R: [-∞, ∞]

48.

What is the period of y = 4Cos(2x)?

a)

4π

b)

π

c)

2π

d)

π/2

49.

which value represents amplitude in the function y = asin(bx-h) + k

a)

a

b)

b

c)

h

d)

k

50.

The __________ represents the distance above or below the midline of a sine or cosine graph; we always take the absolute value of this height.

a)

Period

b)

Frequency

c)

Extreme Values

d)

Amplitude

51.

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

52.

a)

$y=2\sin4x+1$

b)

$y=2\cos4x+1$

c)

$y=-2\cos3x-1$

d)

$y=-2\sin4x+1$

53.

a)

$y=-3\sin x-2$

b)

$y=3\sin x-2$

c)

$y=3\cos x-2$

d)

$y=-3\cos x-2$

54.

a)

$y=-\cos3x+2$

b)

$y=\cos2x+3$

c)

$y=-\cos3x+1$

d)

$y=\sin3x+2$

55.

What is the amplitude of the equation?

y=-3\sin2x-1

a)

3

b)

-3

c)

2

d)

-1

56.

Find the measure of the indicated angle.

a)

9.39

b)

55.2

c)

20.2

d)

19.4

57.

Find the measure of the missing angle.

a)

64^o

b)

26^o

c)

61^o

d)

.008^o

58.

Solve for the missing angle

a)

50

b)

0.053

c)

36.9

d)

95

59.

Set up the problem...

a)

sin X = 41/28

b)

tan X = 41/28

c)

cos X = 28/41

d)

sin X = 28/41

60.

What is the measure of angle x?

a)

73.74 degrees

b)

16.26 degrees

c)

148 degrees

d)

180 degrees

Graph of Trig Functions & Inverse Functions

Total questions: 60

Worksheet time: 3hrs 18mins

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