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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.

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Some Thoughts Concentric Circles Comment 2 of 2 |
Is sin(A) = cos(B) then one of two relations hold.
1: A and B are complementary, which implies A+B = pi/2 +/- 2*pi*n (n is an integer)
2: A is a phase shift of B, which implies A-B = pi/2 +/- 2*pi*n

In the first case, the equation can be simplified to a set of concentric circles (x+1/2)^2 + (y+1/2)^2 = 1/4+pi/2 + 2*pi*n
In the second case, the equation can be simplified to another set of concentric circles (x-1/2)^2 + (y-1/2)^2 = 1/4+3*pi/2 + 2*pi*n

In both cases the smallest members are found when n=0.
(x+1/2)^2 + (y+1/2)^2 = 1/4+pi/2
(x-1/2)^2 + (y-1/2)^2 = 1/4+3*pi/2

  Posted by Brian Smith on 2018-12-16 21:27:51
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