Question

For what values do maximum r-values occur on the graph the polar equation

r=-3 + 4 cos theta? Note that the maximum r-value occurs at a point that is the maximum distance from the pole.

Answer 1

the correct answer is d.pi

Explanation:

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Answer 2

We have the function:

r = -3 + 4*cos(θ)

And we want to find the value of θ where we have the maximum value of r.

For this, we can see that the cosine function has a positive coeficient, so when the cosine function has a maximum, also does the value of r.

We know that the meaximum value of the cosine is 1, and it happens when:

θ = 2n*pi, for any integer value of n.

Then the answer is θ = 2n*pi, in this point we have:

r = -3 + 4*cos (2n*pi) = -3 + 4 = 1

The maximum value of r is 7

(while you may have a biger, in magnitude, value for r if you select the negative solutions for the cosine, you need to remember that the radius must be always a positive number)