# 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.

## A step-by-step guide tosketching 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 forSketching Trigonometric Graphs

### Graph each trigonometric function.

• $$\color{blue}{y=\frac{1}{2}\:cos\:2\:\theta}$$
• $$\color{blue}{y=\:3\:cot\:\theta}$$
• $$\color{blue}{y=\frac{1}{2}\:cos\:2\:\theta}$$
• $$\color{blue}{y=\:3\:cot\:\theta}$$

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