Finding the Bounds of Theta for a Double Integral

[jinksys]

Example:
Use a double integral to find the area of the region:
One loop of the rose r = Cos[3 theta]

Finding the bounds of r is easy, 0 to Cos[3x]. However, I usually get the bounds of theta wrong. How do I find the bounds of theta without using a graphing calculator and guessing. The only method I currently know of is to solve Cos[3 theta]=0, but that gives me unnecessary solutions, like Pi/2 when the bounds really are -Pi/6 to Pi/6.

 

[tiny-tim]

Hi jinksys!

(have a pi: π and a theta: θ )

Use a double integral to find the area of the region:
One loop of the rose r = Cos[3 theta]
…
The only method I currently know of is to solve Cos[3 theta]=0, but that gives me unnecessary solutions, like Pi/2 when the bounds really are -Pi/6 to Pi/6.

That method is right!

Cos3θ = 0 gives you ±π/6, ±3π/6 (=±π/2), and ±5π/6 …

so just chose any two adjacent ones,

such as {±π/6}, or {π/6,π/2}