Trigonometric Graphs - A-Level Maths by StudyWell

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 $\sin(\theta)$

sin

The graph of $\cos(\theta)$

cos

The graph of $\tan(\theta)$

tan

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:

trigcoordinates

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

Solomon Trig Graph Questions

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