calculus

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Find a function of the form f(x)=A sin(B[x−C])+D whose graph is the sine wave shown above. The curve goes through the points (−5,0) and (1,0).
If needed, you can enter π=3.1416... as 'pi' in your answer.

f(x)=

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  1. There are many curves which go through those two points.
    Lat's make it easy and say that we have a sine curve of period 12, crossing the x-axis at the two points. That means we have one arch of the curve (1/2 period).
    If we pick (-5,0) as our starting point, then
    f(x) = sin(π/12 (x+5))
    That gives us A=1 and D=0
    I'll let you decide whether you want to complicate things, such as, what if D is not zero?

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