Question

How would you describe the graphs of the sine and cosine functions? The sine and cosine functions are periodic functions. What does it mean to be a periodic function?

Answer 1

The sine and cosine functions are wave-like functions that repeat themselves on the plane an infinite number of times. The fundamental difference between the two functions is that the valley of the sine function is intersected by the y-axis. In contrast, the crest of the cosine function intersects the y-axis.

Given a function f(x)

`f(x)=\sin (ax)`

We can find its period using the formula below

`\text{period}=(2\pi)/(a)`

where the 2pi term is in radians.

The period of the function is the x-distance needed for the function to complete a cycle.

A periodic function is a function that repeats its values at regular intervals (2pi/a as we found above)