How do I rewrite y = sinx + (sqrt(3))*(cosx) into the form of sinx(a+b)?

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- May 26th 2009, 05:38 PMNevershRewriting an equation into the form of Sin(a+b)
How do I rewrite y = sinx + (sqrt(3))*(cosx) into the form of sinx(a+b)?

- May 26th 2009, 11:37 PMalexmahone

- May 27th 2009, 06:46 AMHallsofIvy
In general, if you have Asin(x)+ Bcos(x) you can write it as either a sine or cosine function.

sin(a+b)= sin(a)cos(b)+ cos(a)sin(b) so if you can find "b" so that cos(b)= A and sin(b)= B you have it. Of course, in that case, so you must first have . In your problem, A= 1 and so , not 1. That was why alexmahone factored out first.

For any A sin(x)+ B cos(x), We can write where and . Since ,

To write A sin(x)+ B cos(x) as a cosine, use cos(a+b)= cos(a)cos(b)- sin(a)sin(b) and do the same thing.