Pre calc. amplitude,period, phase shift and endpoint?

How do you solve this need help asap, thank you!!

Find amplitude,period, phase shift and endpoint

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

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

1 Answer

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    Lv 5
    7 years ago

    OK small pet peeve, it's PI not PIE the Greek letter not the delicious baked pastry.

    y=a*sin(b(x-c)+d

    y=a*cos(b(x-c)+d

    Amplitude=|a| (if a is negative the function flips around the x-axis)

    Period=2pi/b

    Phase Shift=-c/b (the negative in the function above is part of the function if it is x-c, c is positive if it is x+c, c is negative...WATCH the signs)

    Vertical Shift=d

    to find the endpoints solve: 0≤bx-c≤2pi then put the x-values into the function to find the y-values

    1. Amp=1, Per=2pi/2=pi, Phase shift= -(pi/2)/2=-pi,

    endpoints:0≤1x-pi/2≤2pi or pi≤x≤3pi

    (pi,-1), (3pi,-1)

    2.Amp=2, Per=2pi/(1/2) = 4pi, Phase Shift=0,

    endpoints=0≤1/2x≤2pi or 0≤x≤4pi

    (0,-pi/6), (4pi,-pi/6)

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