# How to get the sum/difference of functions

Can someone please explain how to solve this question:

$f(x)=−3+2\cos(x)$

$g(x)=\cos(x−\pi/4)−2$

Sum of functions: $s(x)=f(x)+g(x)$ Difference of functions: $v(x)=f(x)−g(x)$

Get the sum and difference of functions (both sinusoids), round the answer off to 2 decimal places. We are allowed to use the Ti=84+ (so we can use calc max, calc intersect, etc.)

These are the answers, but can someone please explain how they got them: $s(x)=−5+2.80\cos(x–0.26)$

$v(x)=−1+1.47\sin(x–4.21)$

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Specifically, graph $$y_1 = -3 + 2\cos(x) + \cos(x - \pi/4) - 2$$ then, you could start by finding the min and max, which would help you calculate the amplitude and vertical shift, right? In this case, you should find that amplitude = 2.80, and vertical shift = -5. Then, knowing this, if you plot the line $$y_2 = -5$$ (sometimes called the "sinusoidal axis") you can use the intersection of $y_1$ and $y_2$ to help you find the horizontal shift, and you're done.
Then repeat for $f(x) - g(x)$.