How to Sketch Trigonometric Graphs?

A step-by-step guide to sketching trigonometric graphs

To draw a graph of trigonometric functions, you can follow the following steps:

• If the trigonometric function is of the form\(y=a\:sin\:b\:\theta\), \(y=a\:cos\:b\:\theta\) or \(y=a\:tan\:b\:\theta\) identify the values of a and b and calculate the values of the amplitude and period.
• Create a table of ordered pairs for the points you are plotting. The first value in the ordered pair corresponds to the value of the angle \(θ\), and the values of y correspond to the value of the trigonometric function for the angle \(θ\), for example, \(sin\: θ\), so the ordered pair will be \((θ, sin\: θ)\). The values of \(θ\) can be either in degrees or radians.

Sketching Trigonometric Graphs – Example 1:

Graph the trigonometric function \(y=4 sin 2\:\theta\).

Solution:

First, identify the values of \(a\) and \(b\): \(a=4, b=2\)

Then, calculate the amplitude and period:

amplitude\(=\left|a\right|=\left|4\right|=4\)

period \(=\frac{2\pi }{\left|b\right|}=\frac{2\pi }{\left|2\right|}=\pi\)

Create the table of ordered pairs:

Now, plot the points and connect them with a smooth and continuous curve:

Exercises for Sketching Trigonometric Graphs

Graph each trigonometric function.

• \(\color{blue}{y=\frac{1}{2}\:cos\:2\:\theta}\)

• \(\color{blue}{y=\:3\:cot\:\theta}\)

• \(\color{blue}{y=\frac{1}{2}\:cos\:2\:\theta}\)

• \(\color{blue}{y=\:3\:cot\:\theta}\)