Can you graph?

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1 Answer
Rohan N.
Mar 31, 2018

3/4y=2/3cos(3/5theta)

We have to know what the cosine graph looks

cos(theta)

Min~-1
Max~1
Period= 2pi
Amplitude=1

graph{cos(x) [-10, 10, -5, 5]}

Translation form is f(x)=Acos[B(x-C)]+D

A~ Horizontal stretch, amplitude streches by A
B~ Vertical stretch, Period stretches by 1/B
C~Vertical translation, x values move over by C
D~Horizontal translation, y values move up by D

But this can't help us until we have y by itself so multiply both sides by 4/3 to get rid of it from the LHS (left hand side)

y=4/3*2/3cos(2/3theta)

y=8/9cos(2/3theta)

So the 2/3 is the vertical stretch and it stretches the period by 3/2 so the new period is 3pi

The 8/9 is the horizontal stretch so the amplitude is 8/9 so the max is 8/9 and the min is -8/9

graph{8/9cos(2/3x) [-10, 10, -5, 5]}

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