Solving Superposition Problem: Find a3 and Bint

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The discussion revolves around solving the superposition problem of two harmonic waves represented by u1 and u2, leading to an intensity wave uint. Participants express uncertainty about transforming the initial wave equations into the desired sinusoidal form. There is a suggestion to explore trigonometric identities related to the addition of sine functions, particularly those that yield a sine wave with a phase shift. The "int" subscript is interpreted as referring to intensity, and it's noted that the original waves do not depend on time. The conversation emphasizes the need for mathematical manipulation to achieve the desired results.
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The superposition of two harmonic waves:
u1 = B * sin( a1(r) )
u2 = B * sin( a2(r) )
results in a sinusoidal wave of the form:
uint = Bint * sin( a3(r) )
Find a3 and Bint

I'm not sure what to do. I can't think of any way to get it into that "form". http://scienceworld.wolfram.com/physics/Interference.html (5) on that link gives the form I would expect.
I think the "int" subscript is talking about intensity, and I'm not sure but I don't think either u1 or u2 depend on time.
Can anyone help?
 
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Try looking up some trig identities for sine functions. Is there one involving the addition of two sine waves and getting another sine wave with a phase shift?
 
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