Calculus/Hw. Help.

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Expert: - 1/27/2009


Question
Assume the following and evaluate the given expression

sin(x)= 12/13, 0 < x < x/2

find.
sin(4x)=


I thought you could use the formula of sin (2x) and replace it with a 4, but I don't think that's right because i don't come out with the right answer.

Answer
sin(2x)=2sin(x)cos(x)
Here we have sin(x) = 12/13, so the cos(x) = 5/13.

{ you know, if one leg is 12 and the hypoteneuse is 13, the other leg is 5, which I just mentioned in the last problem }

This would mean that the sin(2x) = 2(12/13)(5/13) = 120/169.

With angle 2x, the far side is 120, the hypoteneuse is 169,
and the near side is root(169^2 - 120^2) = root(28,561 - 14,400)
= root(14,161). Using this, the cos() of that angle can be found.

The sin(4x)=2sin(2x)cos(2x), both of which were just found.

Multiply them together while taking a squareroot and you've got the answer.  

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