# Thread: Help with sinusoidal functions...

1. ## Help with sinusoidal functions...

The equation for sinusoidal functions is $\displaystyle y = a (sin) k (x + \frac{d}{k}) + c$ where

"a" is the vertical stretch / compression
"k" is horizontal stretch / compression
"c" is vertical shift
"d/K" is horizontal shift...

so if a graph is given to me and i need 2 find it's equation... how do i know the horizontal stretch

i scanned this sheet given by my teacher... if u guyz could do one of the questions for me and explain me how to do it...

2. Originally Posted by ruscutie100
The equation for sinusoidal functions is $\displaystyle y = a (sin) k (x + \frac{d}{k}) + c$ where

"a" is the vertical stretch / compression
"k" is horizontal stretch / compression
"c" is vertical shift
"d/K" is horizontal shift...

so if a graph is given to me and i need 2 find it's equation... how do i know the horizontal stretch
The period of the sinusoid is $\displaystyle 2 \pi/k$. So determine the period $\displaystyle \tau$ from the diagram, then solve:

$\displaystyle \tau=\frac{2 \pi}{k}$

RonL