Sin Graph

In this lesson, we will look at graphing the sine function.

We will start with the unit circle.
A unit circle is a circle of radius one unit with its centre at the origin.

For a point (x, y) on the unit circle;

y = sin θ  is known as the sine function.

Using the unit circle, we can plot the values of y against the corresponding values of θ.

The graph of y = sin θ, for 0˚ ≤ θ ≤ 360˚ obtained is as shown:

Properties of the sine function:

• The sine function forms a wave that starts from the origin
• sin θ= 0 when θ = 0˚, 180˚, 360˚.
• Maximum value of sin θ is 1 when θ= 90˚. Minimum value of sin θ is –1 when θ = 270˚. So, the range of values of sin θ is

–1 ≤ sin θ≤ 1

• As the point P moves round the circle in either the clockwise or anticlockwise direction, the sine curve above repeats itself for every interval of 360˚. The interval over which the sine wave repeats itself is called the period.

Example:
The diagram shows a graph of  y = sin x for 0˚ ≤ x  ≤ 360˚, determine the values of p, q and r.

Solution:
In order to answer this type of questions, you will need to remember the general properties (or shape) of a sine graph.

We know that the maximum value of a sine graph is 1. So, p = 1.
We know that for a sine graph, sin θ = 0 for θ= 0˚, 180˚ and 360˚. So, θ= 180˚
We know that for a sine graph, sin θ = –1 for θ= 270˚. So, r = 270˚

Example:
Sketch the graph of y = sin 2x for 0˚ ≤ 2x ≤ 360˚.

Solution:
Set up a table of values for the equation y = sin 2x

Plot the points and join with a smooth curve.

Videos

Graphing basic sine and cosine functions (in degrees)

How to use the unit circle definition of the sine function to make a graph of it? (in radians)

Custom Search

Useful Links:
Trigonometry