(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find the area of the region enclosed by one loop of the curve.

r = sin(10θ)

I can't seem to get the correct answer...I checked every step. I was not sure what to integrate from but the polar graph of sin(10θ) should be similar to polar graph of sin(2θ). From pi/2 to 0?

2. Relevant equations

A = integral(b to a) (1/2)r^2 dθ

half angle formula

(sinθ)^2 = (1/2)(1-cos2θ)dθ

3. The attempt at a solution

A = integral(b to a) (1/2)r^2 dθ = integral(pi/2 to 0) (1/2)r^2 dθ

A = (1/2) integral(pi/2 to 0) (sin(10θ))^2 dθ

A = (1/2) integral(pi/2 to 0) (1/2)(1-cos(20θ))dθ

A = (1/4) integral(pi/2 to 0) (1-cos(20θ))dθ

A = (1/4) [(θ-(1/20)sin(20θ)] (pi/2 to 0)

A = (1/4) [(pi/2-(1/20)sin(20*(pi/2)) - (0 - 0)]

A = (1/4)* (pi/2) = pi/8

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Areas and Lengths in Polar Coordinates

**Physics Forums | Science Articles, Homework Help, Discussion**