# THE 5 POINT METHOD OF GRAPHING THE SINE FUNCTION

**By Susan Hewitt**

The 5 point method of graphing trigonometry functions is a quick, easy way to graph 1 period of the desired function.

**y = a sin (b ( x - s )) + v**

Step 1: Identify all of the constants: a, b, s, and v.

Steo 2: Calculate the PERIOD with the formula :

**2pi / b **or **360 degrees / b**

Step3. Calculate the INTERVAL LENGTH for the 5 points by using the formula :

**PERIOD / 4 **

(There are 5 points & 4 intervals.)

Step 4: Use the "s" value, the phase shift, to calculate the endpoints of the new interval.

The original graphing interval of y = sin(x) is [0, 360].

If s<>0, then the new interval is [ 0 + s, 360 + s ].

Step 5: Build a table starting with 0+s, the first point.

The second point is obtained by adding the INTERVAL LENGTH to the first point.

The third point is calculated by adding the INTERVAL LENGTH to the second point, and so forth for the 5 points.

Step 6: Label the x and y axes with the appropriate values.

Step 7: Plot the 5 points as calculated from the table shown below.

Step 8: Connect the 5 points with a smooth curve.

STUDY THE EXAMPLE BELOW CAREFULLY.

# CLICK HERE TO GO TO THE COMPLETED GRAPH

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Last Modified on March 9,1996

##### Comments / criticism can be sent to :

shewitt@nmu.edu

Copyright 1996 Susan Hewitt