Trigonometric Graphs

The graphs of sin, cos and tan are given below. You will notice that $\theta$ is given in radians. Recall that radians is an alternative to degrees when measuring angles. $360^\circ$ is equivalent to $2\pi$ radians.

The graph of $\tan(\theta)$

Imagine a particle traversing the unit circle in an anti-clockwise fashion where $\theta$ measures the anti-clockwise angle between the particle and the x-axis. cos can be thought of as the x coordinate of the particle and sin the y coordinate:

We can also perform transformations of the trigonometric graphs. See Examples.

Example 1

Sketch the graph of $y=2\cos(\theta)$.

This is a y-transformation – the y coordinates have been multiplied by 2. This stretches the graph by a factor of 2 in the y direction. See more on transformations.

Example 2

Sketch the graph of $y=\sin(2\theta)$.

This is an x-transformation – the x coordinates have been multiplied by 2. This stretches the graph by a factor of a half in the x direction. See more on transformations