Trigonometric Graphs - Amplitude And Periodicity - Brilliant

Home » How To Graph A Trig Function » Trigonometric Graphs - Amplitude And Periodicity - Brilliant

Maybe your like

From the definition of the basic trigonometric functions as \(x\)- and \(y\)-coordinates of points on a unit circle, we see that by going around the circle one complete time \((\)or an angle of \(2\pi),\) we return to the same point and therefore to the same \(x\)- and \(y\)-coordinates. This can be extended for going around the circle any multiple of times \((\)or any angle that is a multiple of \(2\pi).\)

Image courtesy: commons.wikimedia.org Image courtesy: commons.wikimedia.org

For example,

\[0 = \sin (0) = \sin (0 + 2\pi) = \sin (0 + 2 \cdot 2\pi) = \cdots = \sin(0 + k \cdot 2\pi)\]

for any integer \(k\).

This shows the trigonometric functions are repeating. These functions are called periodic, and the period is the minimum interval it takes to capture an interval that when repeated over and over gives the complete function.

The periods of the basic trigonometric functions are as follows:

\[\begin{array}{|c|c|} \hline \text{Function} & \text{Period}\\ \hline \sin (\theta) , \cos ( \theta ) & 2\pi\\ \hline \csc (\theta) , \sec ( \theta) & 2\pi \\ \hline \tan (\theta), \cot ( \theta ) & \pi\\ \hline \end{array}\]

Tag » How To Graph A Trig Function