Let A, B, C be angles of a triangle. Find the maximum value of sin A * sin2 B * sin3 C without using calculus.
The maximum seems to occur at A = 45°, B =~ 63.434949°, giving 0.482990683139955 as the value, which Wolfram Alpha identifies as 27/(25*sqrt(5))=˜0.48299068313995.
mx=0; clc
for a=44.9:.001:45.1
% fprintf('%7.2f ',a)
for b=63.434:.000001:63.435
c=180-a-b;
if c>0
% fprintf('%6.4f ',sind(a)*sind(b)^2*sind(c)^3)
if sind(a)*sind(b)^2*sind(c)^3 > mx
mx=sind(a)*sind(b)^2*sind(c)^3;
asave=a; bsave=b;
end
end
end
% fprintf(' ')
end
mx
asave,bsave
mx =
0.482990683139955
asave =
45
bsave =
63.434949
Edited on May 5, 2025, 9:28 am
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Posted by Charlie
on 2025-05-05 09:27:15 |
computer solution -- no calculus
