Determine the maximum r-values of r=7cos4theta

Maximum value of r = 7

Step-by-step explanation:

We have this function:

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:

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:

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

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

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

hope it