Question

R = a Sin 3thita
Sketch the polar curve​

Answer 1

Step-by-step explanation:

Increasing or decreasing the value of a will only change the radius of the curve.

To find when the curve begins and ends, set r=0, since this is where the curve is at the origin.

If asin3θ=0, then sin3θ=0. Since sinθ=0 at θ=0,π,2π... we see that for sin3θ, it will be 0 at 0,π/3,2π/3...

So, the curve in the first quadrant varies from θ=0 to θ=π/3.

The expression for the area of any polar equation r from θ=α to θ=β is given by 12∫βαr2dθ.

For one loop of the given equation, the corresponding integral is then 12∫π/30(asin3θ)2dθ.

Working this integral:

12∫π/30(asin3θ)2dθ=12∫π/30a2(sin23θ)dθ

Use the identity cos2α=1−2