The plot of sin (x + y) = cos (x² + y²) looks like a collection of an infinite number of circles. Find the angle of intersection between the smallest two circles in this family of circles.

It's possible to estimate the circles in Geogebra as having the equations:

x^2 + x + y^2 + y - π/2 - 1/2 = 0 and
x^2 - x + y^2 - y - (3π)/2 = 0

Then applying this:

http://www.quantumstudy.com/mathematics/circle-13/

Working through and cancelling quite nicely (1/2 - 2π)/sqrt((π+2)(3π+1)) is around -0.78992319...

That is the cosine of an angle around 142.17833485 degrees, corresponding with the observed result.

Edited on December 10, 2018, 6:33 am

Posted by broll on 2018-12-10 06:22:46