Your result, is correct. An easy way to check that is to take x= 0. = (9.219)(0.759)= 7 while obviously = -7.
The question asks me to solve
So I put it into the form :
Then I equate the coefficients:
of cos x: 
of sinx: 
Divide  by  to get:
Square and add  and  to get:
Except that last statement doesn't seem to be true, according to
the answers in my book and when I have a look at the two curves in a
graphing application. I tried in the graphing app and
that seems to be correct...
What have I done wrong? Why am I getting a positive value for
alpha when I should be getting the same number but negative?
The only way I can see to get -49.4 would be by introducing a minus
sign when dividing  by . But I don't see how to justify that.
Have I made a simple error? I can't spot it ...
Any help would be much appreciated, thanks in advance.
I see nothing wrong with your work.
Why are you convinced that alpha must be negative?
I was taught a different approach . . .
Divide by:Solve: .
Let be an angle such that: .
Then we have: .
. . which is equivalent to: .
And we have: .
. . Then: .
Since , then: .
. . Therefore: .
Ah thanks. I was convinced it should be negative because when you give degree values to a graph plotting application that's expecting radian values for it's trig functions , then when you compare the graphs of and they aren't the same... but oddly if you stick a minus sign before the offset, the graphs match up. (Is that just a coincidence?)
So that's what I was doing wrong, I needed to convert the input by multiplying it by pi/180. Thank you both again, and it was interesting to see an alternative way to get to rsin(x+alpha).