Question 809616: Please help me with this Calculus II question:
Find all points of intersection of the given curves. (Assume
0 ≤ θ ≤ π.
Order your answers from smallest to largest θ. If an intersection occurs at the pole, enter POLE in the first answer blank.)
Answer by Edwin McCravy(20060) (Show Source):
You can put this solution on YOUR website! Please help me with this Calculus II question:
Find all points of intersection of the given curves. (Assume
0 ≤ θ ≤ π.
Order your answers from smallest to largest θ. If an intersection occurs at the pole, enter POLE in the first answer blank.)
Here are the curves:
r = cos 3θ, r = sin 3θ
cos 3θ = sin 3θ since both = r
Divide both sides by cos 3θ
 
1 = tan(3θ)
So 3θ has referent angle 45° or , The tangent is positive in
QI and QIII
Since we are requiring that 0 ≤ θ ≤ π, that means that
0 ≤ 3θ ≤ 3π
So 3θ can be , , and
So θ can be , , and , which reduces to
We find the value of r for each of those three values for θ, by substituting
in either equation for r
when θ = ,r = cos 3θ = cos = cos =
So the first point is (r,θ) =
when θ = ,r = cos 3θ = cos = cos =
So the second point is (r,θ) =
when θ = ,r = cos 3θ = cos =
So the third point is (r,θ) =
Edwin
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