Pre calc amplitude, phase shift, endpoint?

How do you solve this?

Find the amplitude, period, phase shift and endpoint then graph the following functions.

1). y=cos2( x- (pie/2))

2). y=2sin(1/2)x - (pie/6)

2 Answers

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  • 7 years ago
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    Okay, we just learned this in my class so hopefully I can explain this well enough.

    This is the generic equation for both of sine and cosine: y= +or- a sin[+or- b(x-c)] + d. It is the same for cos except instead of sin it is cos.

    The amplitude of the graph is the absolute value of a.

    The period is 2pi/absolute value of b

    The phase shift of the graph is c

    The end behavior is determined by the leading coefficient so if a is - then the end behavior is -

    For #1

    amplitude= 1

    period= pi

    phase shift= -pi/2

    end behavior= positive

    Now see if you can do # 2 by yourself

    Hope I helped :)

  • 7 years ago

     

    1.) Basic Cosine Function:

    y = a Cos (bx - c) + d, where

    Parameters:

    Amplitude = a

    Period = (2 / b) 'π'

    Phase Shift = (- c / π) 'π'

    y-intercept = d

    y = Cos 2[x - (π/2)], or

    y = Cos (2x - π)

    a = 1

    b = 2

    c = π

    d = 0

    Amplitude = 1

    ¯¯¯¯¯¯¯¯¯¯¯

    Period = π

    ¯¯¯¯¯¯¯¯¯

    Phase = - 1

    ¯¯¯¯¯¯¯¯¯¯

    2.) Basic Sine Function:

    y = a Sin (bx - c) + d

    Parameters are the same as in Problem 1 above, so

    y = 2 Sin (0.5x - π/6)

    a = 2

    b = 0.5

    c = π/6, or 0.524

    d = 0

    Amplitude = 2

    ¯¯¯¯¯¯¯¯¯¯¯¯

    Period = 4π

    ¯¯¯¯¯¯¯¯¯¯

    Phase = (- π/6) / π, or (- π/2) π

    ¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯

     

    Source(s): 5/4/14
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