Ch. 2 Graphs of the Trigonometric Functions; Inverse Trigonometric Functions

2.1 Graphs of Sine and Cosine Functions

1 Understand the Graph of y = sin x

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine the amplitude or period as requested. 1) Amplitude of y = -2 sin x

A) 2 B) -2π C) π 2

D) 2π

2) Period of y = -4 sin x

A) 2π B) π C) π 4

D) 4

3) Amplitude of y = - 1 3

sin x

A) 1 3

B) 3 C) π 3

D) - 1 3

4) Period of y = - 1 4

sin x

A) 2π B) π C) π 4

D) - 1 4

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Graph the function. 5) y = sin x

x -2 -  2

y 3

2

1

-1

-2

-3

x -2 -  2

y 3

2

1

-1

-2

-3

A)

x -2 -  2

y 3

2

1

-1

-2

-3

x -2 -  2

y 3

2

1

-1

-2

-3

B)

x -2 -  2

y 3

2

1

-1

-2

-3

x -2 -  2

y 3

2

1

-1

-2

-3

C)

x -2 -  2

y 3

2

1

-1

-2

-3

x -2 -  2

y 3

2

1

-1

-2

-3

D)

x -2 -  2

y 3

2

1

-1

-2

-3

x -2 -  2

y 3

2

1

-1

-2

-3

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Graph the function and y = sin x in the same rectangular system for 0 ≤ x ≤ 2π.

6) y = 1 4

sin x

x  2

y

3

-3

x  2

y

3

-3

A)

x  2

y

3

-3

x  2

y

3

-3

B)

x  2

y

3

-3

x  2

y

3

-3

C)

x  2

y

3

-3

x  2

y

3

-3

D)

x  2

y

3

-3

x  2

y

3

-3

2 Graph Variations of y = sin x

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

Determine the amplitude or period as requested.

1) Amplitude of y = -5 sin 1 2

x

A) 5 B) 5π 2

C) π 5

D) 4π

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2) Amplitude of y = -5 sin 2x

A) 5 B) 5 2

C) π 5

D) π 2

3) Period of y = sin 5x

A) 2π 5

B) 5 C) 2π D) 1

4) Period of y = -4 cos 1 3

x

A) 6π B) -4 C) 4π 3

D) π 3

5) Period of y = -5 sin 4πx

A) 1 2

B) π 2

C) 2 D) 4π

6) Period of y = 9 4

cos 4π 3

x

A) 3 2

B) 8π 3

C) 9π 2

D) 2 9

7) Period of y = 5 sin 3x - π 2

A) 2π 3

B) 3π 2

C) 2 3

D) 3 2

8) Period of y = -3 sin (8πx + 4π)

A) 1 4

B) π 4

C) 4 D) 8π

Determine the phase shift of the function.

9) y = 1 4

sin (4x + π)

A) π 4

units to the left B) π 4

units to the right

C) - π 4

units to the left D) π units to the left

10) y = -4 sin x - π 4

A) π 4

units to the right B) π 4

units to the left

C) -4 units up D) -4 units down

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11) y = 5 sin 4x - π 2

A) π 8

units to the right B) π 2

units to the left

C) 5π units up D) 4π units down

12) y = 3 sin 1 2

x - π 2

A) π units to the right B) π 2

units to the right

C) π 4

units to the left D) π 3

units to the left

13) y = 1 2

sin (πx + 3)

A) 3 π

units to the left B) π 3

units to the right

C) - π 3

units to the left D) 3 units to the left

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Graph the function. 14) y = -2 sin 3x

x -2 -  2

y

3

-3

x -2 -  2

y

3

-3

A)

x -2 -  2

y

3

-3

x -2 -  2

y

3

-3

B)

x -2 -  2

y

3

-3

x -2 -  2

y

3

-3

C)

x -2 -  2

y

3

-3

x -2 -  2

y

3

-3

D)

x -2 -  2

y

3

-3

x -2 -  2

y

3

-3

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15) y = -3 sin 1 2

x

x -2 -  2

y

3

-3

x -2 -  2

y

3

-3

A)

x -2 -  2

y

3

-3

x -2 -  2

y

3

-3

B)

x -2 -  2

y

3

-3

x -2 -  2

y

3

-3

C)

x -2 -  2

y

3

-3

x -2 -  2

y

3

-3

D)

x -2 -  2

y

3

-3

x -2 -  2

y

3

-3

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16) y = 4 sin x + π 2

x - -2

 2 

y

3

-3

x - -2

 2 

y

3

-3

A)

x - -2

 2 

y

3

-3

x - -2

 2 

y

3

-3

B)

x - -2

 2 

y

3

-3

x - -2

 2 

y

3

-3

C)

x - -2

 2 

y

3

-3

x - -2

 2 

y

3

-3

D)

x - -2

 2 

y

3

-3

x - -2

 2 

y

3

-3

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17) y = 3 4

sin x + π 3

x - -2

 2 

y

3

-3

x - -2

 2 

y

3

-3

A)

x - -2

 2 

y

3

-3

x - -2

 2 

y

3

-3

B)

x - -2

 2 

y

3

-3

x - -2

 2 

y

3

-3

C)

x - -2

 2 

y

3

-3

x - -2

 2 

y

3

-3

D)

x - -2

 2 

y

3

-3

x - -2

 2