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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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1 Answer 1

Well, if you can use your calculator's graphing utility to do this, you could try graphing the sum and difference, then use the tools to find the amplitude, vertical shift, and horizontal (phase) shift, right? (and note that the period doesn't change, so you don't have to worry about this)

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 $f(x) - g(x)$.

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