Question

Determine the maximum r-values of r=7cos4theta

Answer 1

Answer:

Maximum value of r = 7

Step-by-step explanation:

We have this function:

$r=7\cos(4\theta)$

and we want to calculate the maximum values for r.

This can be done by deriving, but there is a simpler way.

If we look at the function, the maximum values of r will be found when the cosine function is maximum.

The maximum values for the cosine function is 1, so the maximum values for r are:

$r_{max}=7\cdot 1=7$

This maximum values happen when the cosine function has a value of 1.

We know that this happens for every natural number n that satisfies:

$\cos(\dfrac{n\pi}{2})=1$

Then, we can calculate the values of theta that satisfy this condition:

$4\theta=\dfrac{n\pi}{2}\\\\\\\theta=\dfrac{n\pi}{8}$

For every natural n, when theta has a value of (nπ/8), the values of r are maximum.