Asked by Anonymous
What is the area of the inner loop of r = 3+6sinΘ?
Answers
Answered by
Steve
you need to find the angles θ which bound the inner loop.
3+6sinθ = 0 when sinθ = -1/2
So, the loop is traced out when 7π/6 <= θ <= 11π/6
So, the area inside the loop is
∫[7π/6,11π/6] 1/2 r^2 dθ
= ∫[7π/6,11π/6] 1/2 (3+6sinθ)^2 dθ = 9π-(27√3)/2
3+6sinθ = 0 when sinθ = -1/2
So, the loop is traced out when 7π/6 <= θ <= 11π/6
So, the area inside the loop is
∫[7π/6,11π/6] 1/2 r^2 dθ
= ∫[7π/6,11π/6] 1/2 (3+6sinθ)^2 dθ = 9π-(27√3)/2
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.