The document provides instructions for sketching a sinusoidal graph in 3 steps: 1) Identify the key characteristics of the sinusoidal function, including median line, amplitude, period, and start point. 2) Draw the median line and mark the start, end, maximum, and minimum points. 3) Join the points with a smooth curve. It then gives an example sinusoidal function to sketch.

1. Sketching a Sinusoidal Graph
• First identify:
Median line (d)
Maximum value (d+a)
Minimum value (d-a)
Period (2л/b)
Start point (-c,d) or (-c/b,d) if b is in the bracket
• Draw the median line on the graph.
• Mark a point on the graph at the start point.
• Mark another point on the graph at the end point, which will be the
start point plus the length of the period.
• Divide the horizontal axis into 4 equal sections beginning at the start
point and finishing at the end point.
• Mark a point on the median line half way between the start point and
the end point.
• Mark a maximum point between the start point and the half way point.
• Mark a minimum point between the half way point and the end point.
• Join the points with a smooth curve.
Example:
Sketch y = 4 sin 2 (x -л) - 2
Assignment:
Sketch the following graphs:
a. y = 2 sin (x - л/2) - 1
b. y = sin 2л x
c. y = -3 sin (2x + л/3)