1. ## Simplifying trigonometric function

Hi,

I hope someone can help. I'm trying to "simplify" y=√2sin(π(x-2.25)) to sinπx - cosπx.

I found the steps online:
line 1 - y=√2sin(π(x-2.25))
line 2 - y=√2sin(πx-2.25pi)
line 3 - y=√2sin(sinπxcos2.25π-sin2.25picosπx)
line 4 - y=√2sin(sinπxcos(2pi+(pi/4)) - sin(2π+(π/4))cospix)
line 5 - y=√2sin((1/√2)sinπx - (1/√2)cospix)
line 6 - sinπx - cosπx

I understand the steps entirely up until and not including line 5. Could someone please explain this to me? I would really appreciate it!

2. ## Re: Simplifying trigonometric function

$y=\sqrt{2} \cdot \sin\left(\pi x - \dfrac{9\pi}{4}\right)$

$y= \sqrt{2} \bigg[\sin(\pi x)\cos\left(\dfrac{9\pi}{4}\right) - \cos(\pi x) \sin\left(\dfrac{9\pi}{4}\right)\bigg]$

note that $\cos\left(\dfrac{9\pi}{4}\right) = \sin\left(\dfrac{9\pi}{4}\right) = \dfrac{\sqrt{2}}{2}$ ...

$y = \sqrt{2} \cdot \dfrac{\sqrt{2}}{2} \bigg[\sin(\pi x) -\cos(\pi x) \bigg]$

$y = \sin(\pi x) - \cos(\pi x)$

btw ... when are you gonna start posting up in LaTeX?

3. ## Re: Simplifying trigonometric function

Okay makes sense, thanks for your help. And I wasn't aware of LaTex, but I'll start using it from now on.

4. ## Re: Simplifying trigonometric function

Originally Posted by otownsend
Okay makes sense, thanks for your help. And I wasn't aware of LaTex, but I'll start using it from now on.
To see how others have formatted posts, you can click "reply with quote" and you will see what they wrote (including their LaTex code).