Question

How do I graph y= 4/3 cos 3/2x ?

Answer 1

First...you function y is a cosine signal ....since cosine is always bounded between +1 and -1, then your max and min values are 4/3 and -4/3 respectively.

Answer 2

Now you can sketch a cosine wave with the above max and min values.

Answer 3

You are only left to place the x-axis zero-corssings

Answer 4

You do that by letting

cos(3/2x)=0

Answer 5

This can happen at

(3/2)x = integer multiples of \[\pi/2\]

Answer 6

\[(3/2)x=k*\pi/2\]

Answer 7

so

\[x=k \pi/3\]

Answer 8

\[x=...,-2\pi/3,-\pi/3,\pi/3,2\pi/3,...\]