math
posted by lauren .
find all solutions in the interval [0,2 pi)
sin(x+(3.14/3) + sin(x 3.14/3) =1
sin^4 x cos^2 x
Since sin (a+b) = sina cosb + cosb sina
and
sin (ab) = sina cosb  cosb sina,
the first problem can be written
2 sin x cos (pi/3)= sin x
The solution to sin x = 1 is x = pi/2
For your other problem
sin^4 cos^2 x = sin^4 x(1  sin^2x)=0
The solutions are sin x = 0 and sin^2 x = 1. That would correspond to x=0, pi/2, pi, and 3 pi/4
the answer is $344,000.000
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