Question

Show that the following rectangular form x^2+y^2=2xy can be expressed as 1 = sin(2) in polar form.

Answer 1

Explanation:

substitute x = r*cos(θ), y = r*sin(θ) ==> r²(cos²(θ) + sin²(θ)) = 2r²cos(θ)sin(θ). Cancel the r² on both sides. On the left, use pythagorean identity cos²(θ) + sin²(θ) = 1. On the right apply double angle identity sin(2θ) = 2cos(θ)sin(θ).

This yields 1=sin(2θ). (I assume you meant to type sin(2θ) on the right hand side of the equation).