Combining Sine and Cosine Functions for f-g: Homework Example

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Homework Statement

Determine a sine function, f, and a cosine function, g, such that y = sqrt2sin(pi(x-2.25))
can be written in the form of f-g.

Homework Equations

(f-g)(x) = f(x) - g(x)

The Attempt at a Solution

I think that you should sub in the y= equation so that you get:
sqrt2sin(pi(x-2.25)) = f(x) - g(x)

and then sub in any X value? I really don';t know

 

[HallsofIvy]

Do you understand what the question is asking? You are to find a function f(x)= A sin(wx) and a function g(x)= B cos(vx) for constants A, B, w, and v. Since you don't yet know what f and g are, putting values of x into what you have won't tell you anything.

What you need is the identity sin(a- b)= sin(a)cos(b)- cos(a)sin(b). That way, sin(pi(x- 2.25)= sin(pix- 2.25pi)= sin(pix)cos(2.25pi)- cos(pix)sin(2.25pi), a constant times a sine function of x and a constant times a cosine function of x.

 

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Sorry for my ignorance, I understand what you explained previously, but I don't understand what I get for f(x) and g(x)?