Consider this equation:
sin(sin(sin(sin(x))) = cos(cos(cos(cos(x)))
where x is a real number considered in radians.
Does there exist at least one solution to the given equation?
- If so, provide all possible solutions to the given equation.
- If not, prove, with valid reasoning that there does not exist any solution to the given equation.
sym x
fplot(@(x)sin(sin(sin(sin(x)))))
hold on
fplot(@(x)cos(cos(cos(cos(x)))))
grid on
plots the two functions over one cycle.
See the graph here, where are shown somewhat more than the 2*pi cycle length and no intersection is found.
That completes the puzzle which asked only for real solutions.
Wolfram Alpha supplies complex solutions:
x ~= -4.712388980384689857687898276... - 1.210684044891034049791826355... i
x ~= -4.712388980384689857687898276... + 1.210684044891034049791826355... i
x ~= 0.7568871373475711187264023347... - 0.6101549969203425542976000508... i
x ~= 0.7568871373475711187264023347... + 0.6101549969203425542976000508... i
4.712388980384689857687898276 is 3*pi/2 but Wolfram Alpha wasn't able to identify the other numbers in these solutions.
Edited on June 5, 2023, 2:19 pm
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Posted by Charlie
on 2023-06-05 13:43:41 |
computer solution
