Respuesta :
Answer:
Maximum value of r = 7
Step-by-step explanation:
We have this function:
[tex]r=7\cos(4\theta)[/tex]
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:
[tex]r_{max}=7\cdot 1=7[/tex]
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:
[tex]\cos(\dfrac{n\pi}{2})=1[/tex]
Then, we can calculate the values of theta that satisfy this condition:
[tex]4\theta=\dfrac{n\pi}{2}\\\\\\\theta=\dfrac{n\pi}{8}[/tex]
For every natural n, when theta has a value of (nπ/8), the values of r are maximum.
