Difference of functions thinking problem

[I Like Pi]

Homework Statement

Determine a sine function, f, and a cosine function, f, such that y= √2 sin (π(x-2.25)) can be written in the form of f-g.

Homework Equations

The Attempt at a Solution

well.. i know that:
= sinx - cosx
= sinx - (-sin(π/2-x))
= √2 sin(x + π/4)

that's as close i can get it is there an algebraic way to determine this?

thank you!

 

[symbolipoint]

You almost have all of it. There is a subtraction of one function from another function.
f(x)=sin(x). g(x)=$$\sqrt{2}$$sin(x+$$\pi$$/4)

Can you convert g(x) into a cosine function?

 

[I Like Pi]

You almost have all of it. There is a subtraction of one function from another function.
f(x)=sin(x). g(x)=$$\sqrt{2}$$sin(x+$$\pi$$/4)

Can you convert g(x) into a cosine function?

okay.. but sinx - $$\sqrt{2}$$sin(x+$$\pi$$/4) doesn't equal √2 sin(π(x-2.25))

 

[symbolipoint]

Unfortunately, I misunderstood the question and this may have mislead you. I hope someone else understands the original question better than I did and has stronger skill with Trignometry and can give better help.

 

[LeonhardEuler]

You started with a good formula. Just change the period and the phase on the equation you started with, and you'll be good.

 

[HallsofIvy]

sin(a+ b)= sin(a)cos(b)+ cos(a)sin(b)

Here, you have $a= \pi x$ and $b= -2.25\pi$.