Question

Trace curve of r=2+3cos (theta)

Answer 1

Find the area enclosed by the curve:

r=2+3cosθr=2+3cos⁡θ

Here's my steps:

since when r=0r=0, cosθ=0cos⁡θ=0 or cosθ=arccos(−2/3)cos⁡θ=arccos⁡(−2/3).

so the area of enclosed by the curve is 2*(the area bounded by θ=arccos(−2/3)θ=arccos⁡(−2/3) and θ=0θ=0)

the answer on my book is 55–√+（17/2）∗arccos(−2/3)55+（17/2）∗arccos⁡(−2/3)

I have no idea why there is a 55–√55 since arccos(−2/3)=2.300523984arccos⁡(−2/3)=2.300523984 on my calculator.

Answer 2

This is ur answers hope it will help u