Free Printable Graphs of Trig Functions

1.

The period of a sine graph in the form $y=a\sin\left(bx\right)+d$

a)

It's always $2\pi$

b)

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

c)

$b\cdot2\pi$

d)

$b+2\pi$

2.

What is the period of
y= -3sin(x)

a)

π

b)

2π

c)

3π

d)

4π

3.

What is the period of
y=cos(3x - π) - 5?

a)

π/3

b)

π/6

c)

2π/3

d)

2π/6

4.

What is the period of this function?

a)

4π

b)

2π

c)

½π

d)

½

5.

What is the period of the graph?

a)

π

b)

π/2

c)

2π

d)

4π

6.

What is the period of the graph?

a)

2Pi

b)

Pi

c)

Pi/2

d)

Pi/4

7.

Which of the following functions does NOT have a period of 2π?

a)

y = sin x

b)

y = tan x

c)

y = csc x

8.

What is the period of the graph?

a)

8π

b)

4π

c)

π

d)

2π

9.

What is the period of this function?

a)

\frac{\pi}{4}

b)

$\frac{\pi}{2}$

c)

$\pi$

d)

$2\pi$

10.

The period of this graph is π, therefore b =

a)

2

b)

1

c)

π

d)

½

11.

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

12.

What is the amplitude of the function
f(x) = -3cos x ?

a)

-3

b)

3

c)

6

d)

-6

13.

What is the phase shift?
y=-2sin(x-π)

a)

π left

b)

π right

c)

none

d)

2π right

14.

Which value represents a vertical shift in the following function y=a*sin(bx - c)+d?

a)

a

b)

b

c)

c

d)

d

15.

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

a)

y=6sin(8x)

b)

y=6sin8(x-1)

c)

y=6sin1/4x

d)

y=6sinx

16.

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

a)

y=6sin(8x)

b)

y=6sin(8x-8)

c)

$y=6\sin\left(\frac{1}{4}x\right)$

d)

y=6sinx

17.

Write an equation for the cosine function with amplitude 3, period $2\pi$ , phase shift of $\pi$ to the right, and vertical shift of 5.

a)

$y=5\cos(x-\pi)+3$

b)

$y=3\cos(x-\pi)+5$

c)

$y=3\cos(2x-\pi)+5$

d)

$y=5\cos(2x-\pi)+3$

18.

How many "key points" should be included in every cycle/period of a sine or cosine graph?

a)

As many as I want

b)

It depends on the graph

c)

4

d)

5

19.

To re-scale the x-axis with new intervals...

a)

Take 2π/B

b)

Take the B value from the equation

c)

Take Period divide it by 4

d)

The scale doesn't really matter

20.

What are the x values of the five key points of $y=2\sin\left(4x\right)$ ?

a)

$0,\ \frac{\pi}{8},\ \frac{\pi}{4},\ \frac{3\pi}{8},\frac{\pi}{2}$

b)

$0,\ \frac{\pi}{4},\ \frac{\pi}{2},\ \frac{3\pi}{4},\ \pi$

c)

$0,\ \frac{\pi}{2},\ \pi,\ \frac{3\pi}{2},\ 2\pi$

d)

$0,\ \pi,\ 2\pi,\ 3\pi,\ 4\pi$

21.

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: [-∞, ∞]

22.

Which functions have asymptotes?

a)

y=sinx

b)

y=cscx

c)

y=cotx

d)

y=secx

e)

y=cosx

23.

Which value is NOT defined?

a)

$\tan0$

b)

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

c)

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

d)

$\tan\left(2\pi\right)$

24.

The graph of y = tan(x) has an asymptote at x =

a)

0

b)

$\pi$

c)

$\frac{\pi}{2}$

d)

$3\pi$

25.

The graph of y = sec(x) has an asymptote at x =

a)

0

b)

$\pi$

c)

$\frac{\pi}{2}$

d)

$3\pi$

26.

Which parent functions include the point (0, 1)?

a)

sine and cosecant

b)

cosine and secant

c)

cosine, secant, and tangent

d)

sine, cosecant, and cotangent

27.

Which parent functions include the point (0, 0)?

a)

sine and cosecant

b)

cosine and secant

c)

cosine, secant, and cotangent

d)

sine and tangent

28.

What is the range of y = 2sec(x)?

a)

[-2,2]

b)

[-5,-2] U [2,5]

c)

[-∞,-2] U [2, ∞]

d)

😎

29.

What is the equation of graph?

a)

y = sin 5x

b)

y = cos 5x

c)

y = 5 sin x

d)

y = 5 cos x

30.

a)

A

b)

B

c)

C

d)

D

31.

Choose a correct equation for this graph given the period is 4π.

a)

y = 2 + cos(½x)

b)

y = 2 + 2cos(½x)

c)

y = 4 + 2cos(½x)

d)

y = 4 + 2cos(4x)

32.

Which equation?

a)

y= – cos(2x)

b)

y= cos(2x)

c)

y= cos(½x)

d)

y= (−½)cosx

33.

What is the y-intercept of the graph?

a)

(0, -3)

b)

(0, 2)

c)

(0, -2)

d)

(0, 3)

34.

Choose an equation for the blue graph.

a)

y = –2cosx + 1

b)

y = –2sec x + 1

c)

y = 2csc x + 1

d)

y = –cscx + 1

35.

Choose the correct equation for the graph.

a)

$y=\sin\left(x\right)$

b)

$y=\sec\left(x\right)$

c)

$y=\csc\left(x\right)$

d)

$y=\tan\left(x\right)$

e)

$y=\cos\left(x\right)$

36.

Choose the correct equation for the graph.

a)

$y=\sin\left(x\right)$

b)

$y=\sec\left(x\right)$

c)

$y=\csc\left(x\right)$

d)

$y=\tan\left(x\right)$

e)

$y=\cot\left(x\right)$

37.

Choose the correct equation for the graph.

a)

$y=\cot\left(x\right)$

b)

$y=\sec\left(x\right)$

c)

$y=\csc\left(x\right)$

d)

$y=\tan\left(x\right)$

e)

$y=\cos\left(x\right)$

38.

Which equation best represents the graph?

a)

y = 2 sin(2x) - 3

b)

y = 2 cos(2x) - 3

c)

y = 2 sin(x) - 3

d)

y = -2 sin (2x) - 3

39.

Which equation best fits the graph?

a)

y = 2 sin(1/4 t) - 1

b)

y = 3 sin(t) - 1

c)

y = -2 sin(1/4 t) - 1

d)

y = 2 cos(1/4 t) - 1

40.

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

41.

Determine an equation for this graph:

a)

y=sec(x)

b)

y=2sec(x)

c)

y=2csc(x)

d)

y= csc(2x)

42.

Evaluate the function: arcsin(-1/2)

a)

π/3

b)

π/6

c)

5π/6

d)

-π/6

43.

Evaluate: cos^-1(√3/2)

a)

π/3

b)

2π/3

c)

π/6

d)

5π/6

44.

tan(sin^-1(-1/2))

a)

√3

b)

√3/3

c)

-√3

d)

-√3/3

45.

Domain of function $\sin^{-1}x\ is$

a)

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

b)

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

c)

$\left(-1,1\right)$

d)

$\left[-1,1\right]$

46.

Range of function $\cos^{-1}x\ is$

a)

$\left[0,\ \pi\right]$

b)

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

c)

$\left(-1,1\right)$

d)

$\left[-1,1\right]$

47.

Range of function $\sin^{-1}x\ is$

a)

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

b)

$\left(-\frac{\pi}{2},\frac{\pi}{2}\right)$

c)

$\left(-1,1\right)$

d)

$\left[-1,1\right]$

48.

a)

A

b)

B

c)

C

d)

D

49.

a)

A

b)

B

c)

C

d)

D

50.

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

a)

$\frac{\pi}{6}$

b)

$\frac{1}{2}$

c)

$60\degree$

d)

no solution

51.

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

a)

$\frac{\pi}{4}$

b)

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

c)

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

d)

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

52.

cos[arccos(-2)]

a)

-2

b)

no solution

c)

2

d)

$\frac{1}{2}$

53.

arctan[tan( $\frac{5\pi}{4}$ )]

a)

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

b)

$\frac{\pi}{4}$

c)

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

d)

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

54.

cos[arccos( $\frac{1}{3}$ )]

a)

3

b)

$\frac{1}{3}$

c)

-3

d)

no solution

55.

arctan[tan( $\frac{2\pi}{3}$ )]

a)

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

b)

$\frac{\pi}{3}$

c)

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

d)

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

56.

Find the exact value of $\cos\left[\arctan\left(-\frac{3}{4}\right)\right]$

a)

$\frac{4}{5}$

b)

$-\frac{4}{5}$

c)

$\frac{3}{5}$

d)

$\frac{5}{4}$

57.

Match each function with its period.

a)

sin(x)

1.

2π

b)

cos(x)

2.

2π

c)

tan(x)

3.

π

d)

cot(x)

4.

π

e)

sec(x)

5.

2π

58.

Organize these options into the right categories

Categorize the following

cos(x)

sin(x)

sec(x)

tan(x)

cot(x)

csc(x)

Even Functions

Odd Functions

Graphs of Trig Functions

Total questions: 58

Worksheet time: 3hrs 50mins

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