(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The text book problems states: y=cos3x +sin3x and you are to combine it to a single cos function and tell what effect the 3 has. The answer in the back of the book is given as sqrt2*cos(3x-pi/4) and that the 3 means the wave has a horizontal dilation of 1/3.

2. Relevant equations

general solution for a sinusoid y = C+A*cosB(X-D) where C is the axis, A is the amplitude, B is the reciprocal of the period, X is the angle in radians and D is the phase displacement.

3. The attempt at a solution

1. find A using the pythagorean theorem: so from the original equation y=cos3x+sin3x, we get A=sqrt of 1^2+1^2 or the sqrt of 2 (because the coefficients in the above equation are both 1)

2. Find D by finding the inverse tan of 1/1, because the two coefficients in this prob. are both 1. So the inverse tan of 1 is pi/4.

3. Then I substitued pi/4 for D in the general sinusoid equation sqrt of 2 for A, giving me:

y=sqrt2*cosB(x-pi/4)

4. I used the 3's from the original problem as B in my general equation. so now I have:

y=sqrt2*cos3(x-pi/4)

This is what I thought the answer should be....why does the correct answer have the 3 inside the parenthesis like this: y=sqrt2*cos(3x-pi/4)? It seems to me that the 3 should not only be distributed to the X, but should be outside the parenthesis so that it gets distributed over both X and D.

Please help me understand where I'm going wrong.

Thanks so much.

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Homework Help: Confused about how to solve this problem combining sinusoids please help

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