Question

Can you graph?

Answer 1

`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]}