How to Sketch Trigonometric Graphs?
You can sketch trigonometric functions in a few steps. In this step-by-step guide, you will learn how to sketch trigonometric graphs.
![How to Sketch Trigonometric Graphs?](https://www.effortlessmath.com/wp-content/uploads/2023/01/Sketching-Trigonometric-Graphs-512x240.jpg)
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:
![](https://www.effortlessmath.com/wp-content/uploads/2023/01/Untitleda-2.png)
Now, plot the points and connect them with a smooth and continuous curve:
![](https://www.effortlessmath.com/wp-content/uploads/2023/01/Untitled2.png)
Exercises for Sketching Trigonometric Graphs
Graph each trigonometric function.
- \(\color{blue}{y=\frac{1}{2}\:cos\:2\:\theta}\)
![](https://www.effortlessmath.com/wp-content/uploads/2021/12/Graphing-Rational-Expressions-Example-3-4.png)
- \(\color{blue}{y=\:3\:cot\:\theta}\)
![](https://www.effortlessmath.com/wp-content/uploads/2021/12/Graphing-Rational-Expressions-Example-3-4.png)
![This image has an empty alt attribute; its file name is answers.png](https://www.effortlessmath.com/wp-content/uploads/2019/12/answers.png)
- \(\color{blue}{y=\frac{1}{2}\:cos\:2\:\theta}\)
![](https://www.effortlessmath.com/wp-content/uploads/2023/01/Untitledv-2.png)
- \(\color{blue}{y=\:3\:cot\:\theta}\)
![](https://www.effortlessmath.com/wp-content/uploads/2023/01/Untitledaa.png)
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