Question

I have a quick question about the x-axis with trigonometric functions.

Answer 1

well you should ask away

Answer 2

hello?

Answer 3

any changes in trig functions domain indicate a change of period, or sometimes a phase change.

The period change is easy to explain.
For a function y = a sin (bx), the b coefficient affects the period T.
\[T = \frac{ 2\pi }{ b }\]
The period just refers to the distance covered by one complete cycle.

Consider sin x vs sin 2x
The period for sin x is T = 2pi/1 = 2pi and the period for sin 2x is T = 2pi/2 = pi
This means sin x completes one cycle in 2 pi units, while sin 2x completes this in pi units, or half the distance. Their graphs...



Notice that sin 2x completes cycle in half distance meaning you can fit two cycles into the span of 2pi.