# Thread: Thinking question for trig + combining functions

1. ## Thinking question for trig + combining functions

Hi, here's a really tough thinking question that has me totally stumped. Could someone please show me how to approach it?

Determine a sine function, F, and a cosine function, G, such that y= (squareroot of 2)sin(pi(x-2.25)) can be written in the form of F-G.

The solution at the back is:
f(x): sin(pi(x))
g(x): cos(pi(x))

I have no idea where to start...

2. Originally Posted by MATHDUDE2
Hi, here's a really tough thinking question that has me totally stumped. Could someone please show me how to approach it?

Determine a sine function, F, and a cosine function, G, such that y= (squareroot of 2)sin(pi(x-2.25)) can be written in the form of F-G.

The solution at the back is:
f(x): sin(pi(x))
g(x): cos(pi(x))

I have no idea where to start...
first we may be unclear about your notations
is this what you mean

$y=\sqrt{2}\sin{\pi\left(x-2.25\right)}$

$f(x) = \sin{\pi x}$
$g(x) = \cos{\pi x}$

3. Dear MATHDUDE2,

First you should try to simplify y= (squareroot of 2)sin(pi(x-2.25))
by using the formula, Sin(A-B)= SinACosB-SinBCosA. If you find the problem difficult please see the attachment below. Please let me know if you cannot read the attachment or if you have any problems regarding this matter.

Hope this helps.

4. Originally Posted by bigwave
first we may be unclear about your notations
is this what you mean

$y=\sqrt{2}\sin{\pi\left(x-2.25\right)}$

$f(x) = \sin{\pi x}$
$g(x) = \cos{\pi x}$
Yes that's it. Sorry I'm not familiar with the coding stuff...

5. Originally Posted by Sudharaka
Dear MATHDUDE2,

First you should try to simplify y= (squareroot of 2)sin(pi(x-2.25))
by using the formula, Sin(A-B)= SinACosB-SinBCosA. If you find the problem difficult please see the attachment below. Please let me know if you cannot read the attachment or if you have any problems regarding this matter.

Hope this helps.
Hi Sudharaka, thanks for the prompt and very detailed help. I can see the picture fine but I don't understand the 4th and 5th lines. How/why did you split 2.25 into (2 + 1/4)? And what happened from then on?

Thanks again!

6. Dear MATHDUDE2,

Do you know that Sin(2pi+A)=SinA and Cos(2pi+A)=CosA
If you do not know these trignomatic identities please refer any basic trignomatic book or the website List of trigonometric identities - Wikipedia, the free encyclopedia

### determine a sine function, f, and a cosine function, g, such that y=

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