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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