Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004

Introduction to Periodic Motion Ferris Wheel Demonstration – Page 558 of 2nd edition of Haese and Harris textbook. – FerrisWheelUnitCircle32_L.html FerrisWheelUnitCircle32_L.html Temperatures – Tides – Tidesandcurrents.noaa.gov – Pendulums Section 16EF – Periodic and Sine Functions

Vocabulary – Pg 530 Principal Axis – Imaginary line about which the wave oscillates. Maximum Point – Top of crest. Minimum Point – Bottom of trough. Amplitude – Distance between maximum or minimum and the principal axis. Period – Length or time for one complete repetition or cycle.

90º270º180º º - 180º -90º Graph Paper - Label -270º-360º

xsin x 0° 45° 90° 135° 180° 225° 270° 315° 360° Graph y = sin x period = amplitude = 360  1

Graph y = cos x xcos x 0° 45° 90° 135° 180° 225° 270° 315° 360° period = amplitude = 360  1

y = cos xy = sin x

Sketch y = x 2 and then y = (x + 4) 2 – 2

Transforming Graphs Mother Function Relative Function Transformation? y 1 = sin xy 2 = - sin xreflection over x-axis y 1 = sin xy 2 = 4sin xamplitude = 4 y 1 = sin xy 2 = ½sin xamplitude = ½ y 1 = cos xy 2 = 2 + cos xvertical translation 2 units up y 1 = cos xy 2 = -3 + cos xvertical translation 3 units down y 1 = sin xy 2 = sin 2x period = 180  y 1 = sin xy 2 = sin ½x period = 720  DO NOT WRITE THIS DOWN

y = a sin bx + c y = a cos bx + c c = vertical translation Summary:

Without using technology sketch the graph of: y = 2sinx for 0  ≤ x ≤ 360  Example 1

Without using technology sketch the graph of: y = -2sinx for 0  ≤ x ≤ 360  Example 2

State the amplitude and period of: y = 3 cos 2x Example 3

The diagram below shows the graph of: y = – a sin x° + c, 0 ≤ x ≤ 360. Use the graph to find the values of: (a)c (b)a Example 4

The diagram shows the graph of y = sin ax + b. (a)Using the graph, write down the following values: (i) the period (ii)the amplitude (iii) b (b)Calculate the value of a. Example 5

Homework Pg – 16E – #3,#4 Pg – 16F.1 – #1abcd, #3abc, #4ab Pg – 16F.2 – #1abcdefgh, #2ade