Trigonometric Graphs - StudyWell

Trigonometric Graphs

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. $\cos(\theta)$ can be thought of as the x coordinate of the particle and $\sin(\theta)$ the y coordinate:

trigcoordinates

The graphs of $\sin(\theta)$ and $\cos(\theta)$ are given below:

The graph of $\sin(\theta)$

The graph of $\cos(\theta)$

Recall that $\tan(\theta)=\frac{\sin(\theta)}{\cos(\theta)}$ from trigonometric identities. The graph of $\tan(\theta)$ is 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 $\tan(\theta)$

tan

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

Example 1

Sketch the graph of $y=2\cos(\theta)$ .
2costheta
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 $y=\sin(2\theta)$ .
sin2theta
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

Past Trigonometric Exam Questions

We have collated past exam questions on trigonometry so that you may focus your concentration on this particular subject (answers on the back pages). Alternatively, visit our Questions by Topic page to see which topics you can focus on.

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