SOLUTION: For the polar equation {{{r=8}}} cos 3θ, find the maximum value of |r| and any zeros of r. Verify answers numerically.

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Question 1081120: For the polar equation r=8 cos 3θ, find the maximum value of |r| and any zeros of r. Verify answers numerically.
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!

r=8cos%283theta%29 will have maximum values when cos%283theta%29+=+1 and it is for theta+=+%282+pi%2A+n%29%2F3 for integer n where n = 0,1,2,...
so, if cos%283theta%29+=+1=>r=8

check:
n=0->theta+=+%282+pi%2A0+%29%2F3+=0
.
r=8+cos%28+3%2A0%29
r=8+cos%28+0+%29
r=8+%2A1
r=8
8=8+cos%28+0%29-> true

n=1->theta+=+%282+pi%2A1+%29%2F3
.
r=8+cos%28+3%282+pi+%29%2F3%29
+r=8+cos%28+2+pi+%29
r=8+%2A1
r=8
8=8+cos%28+2+pi+%29-> true

n=2->theta+=+%282+pi+%2A2%29%2F3=+%284+pi+%29%2F3
.
r=8+cos%28+3%284+pi+%29%2F3%29
+r=8+cos%28+4+pi+%29
+r=8+%2A1
r=8
8=8+cos%28+2+pi%29-> true