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anonymous
 5 years ago
find 3 coeff. b1, b2, b3 E of R3 such that:
sin(t)cos(2t) = b1sin(t) + b2sin(2t) + b3sin(3t).
i just need a clue of the formula i need to use. thx alot.
anonymous
 5 years ago
find 3 coeff. b1, b2, b3 E of R3 such that: sin(t)cos(2t) = b1sin(t) + b2sin(2t) + b3sin(3t). i just need a clue of the formula i need to use. thx alot.

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anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0It looks like you'd need to check out one of the several double angle formulas for cos(2t) and it should become pretty simple at that point.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0that's what i thought, but it's a linear algebra class so I think it's a little tougher than that.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0waaaa never mind i think it's that simple.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0So, I'm assuming you're being asked to prove that sin(t)cos(2t) is in the span of {sin(t), sin(2t), sin(3t)} or something similar? Yeah, I think in this case it really is going to be simple. Sometimes with Linear Algebra problems are almost so simple that they look hard! :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Of course the real problem is that then there is a problem that looks really simple, but ends up being really difficult and it's not always clear which is which. :)

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0(sin t)(cos (2t)) = (sin t)(1 – 2(sin t)^2) = sin t – 2 (sin t)^3. sin(3t) =sin (2t + t) = sin (2t) cos (t) + cos (2t) sin(t) = … = 3sin t – 4(sin t)^3. sin(2t) = 2(sin t)(cos t). sin (t) = sin (t). So now notice the Left Hand Side has no cosines. This suggests letting b2 = 0. Notice that the Left Hand Side has coefficient 2 on the cubic term. This suggests letting b3 = ½. But if you make b3 equal to 1/2, then it contributes 3*(1/2) to the coefficient of sin t. To compensate, we should let b1 be 1/2. So (1/2, 0, 1/2) is the solution.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0Or is a solution, I'm not sure that it's unique.

anonymous
 5 years ago
Best ResponseYou've already chosen the best response.0thanks a lot i verified my answer and it's for sure correct.
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