Points of Intersection in Polar Areas

[JRangel42]

Homework Statement

The question is to find the area of the region that lies inside both curves. The part I'm specifically having trouble with is finding the points of intersection.

Homework Equations

sin (2∅)

cos (2∅)

The Attempt at a Solution

sin 2∅ = cos 2∅
2 sin ∅ cos ∅ = 1 - sin^2 ∅
2 sin Θ cos Θ + sin^2 Θ = 1
sin Θ(2cos Θ + sin Θ) - 1 = 0

 

[LCKurtz]

Homework Statement

The question is to find the area of the region that lies inside both curves. The part I'm specifically having trouble with is finding the points of intersection.

Homework Equations

sin (2∅)

cos (2∅)

The Attempt at a Solution

sin 2∅ = cos 2∅
2 sin ∅ cos ∅ = 1 - sin^2 ∅
2 sin Θ cos Θ + sin^2 Θ = 1
sin Θ(2cos Θ + sin Θ) - 1 = 0

You don't need the double angle formulas. Divide both sides of your first equation by cos(2∅) to get a single equation involving the tangent function.

 

[JRangel42]

Seriously?! Anyway, thanks for the help. (^O^)