# Thread: Principle behind compressing trig functions

1. ## Principle behind compressing trig functions

Hi!

What's the idea behind compressing functions when graphing, compressing horizontally or vertically:

1. $y = \sec 2x\ \text{versus}\ 2 \sec x$

There is no amplitude, what's the function of the second 2?

2. $y = \sec \frac12x\ \text{versus}\ \frac12 \sec x$

2. ## Re: Principle behind compressing trig functions

Consider the function $y_1 = f(x)$ -- if the constant A is introduced then the function $y_1=Af(x)$ will be stretched vertically by factor A, and the function $y_3=f(Ax)$ will be squeezed horizontally by factor A. Here is an example where $y_1 = sin(x)$ and A = 3. See how $y_2 = 3sin(x)$ is streteched vertically while its period remains the same, and $y_3 = sin(3x)$ is squeezed horizontally while it's height remains the same?