Question

Question #b9a7e

Answer 1

A) r=0 if `theta` is equal to `30^o` or `90^o`

B) the maximum value for r is 2

Explanation:

First we look at the values for the cosine. The possible values are between -1 and 1.

So, for r to be 0 in the equation below, the cosine has to be 0, which happens when the angle being evaluated is either `90^o` or `270^o`. So we have:

`r=2*cos 3theta`

Since 2 is a constant we can take it out and look at:

`0=cos 3theta`

So, since there are only two values were the cosine is equal to 0, we can set those equal to `3theta` and go from there

`3theta=90`
`theta=90/3=30`

`3theta=270`
`theta=270/3=90`

The second part asks what is the highest value of r. Again, with 2 being a constant, the variable is the cosine. It has a maximum value of 1, so, substituting that in the equation we get the maximum r is equal to 2.