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Transcript of Full file at ... Ch. 2 Graphs of the Trigonometric Functions; Inverse Trigonometric Functions 2.1...

  • 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

    Page 1

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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

    Page 2

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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

    Page 3

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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

    Page 4

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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

    Page 5

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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

    Page 6

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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

    Page 7

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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

    Page 8

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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