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Hoops (Posted on 2018-12-09) Difficulty: 4 of 5
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.

No Solution Yet Submitted by Danish Ahmed Khan    
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Mostly guesswork | Comment 1 of 2

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

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