1. Graphs of Sine and Cosine Functions Lesson 2.5

2. 2 Ordered Pairs  Consider the values for x and y in the table to the right  Note Period = 2 π Maximum y values Minimum y values xsin(x)cos(x) -3.14160.0000 -2.6180-0.5000-0.8660 -2.0944-0.8660-0.5000 -1.57080.0000 -1.0472-0.86600.5000 -0.5236-0.50000.8660 0.0000 1.0000 0.52360.50000.8660 1.04720.86600.5000 1.57081.00000.0000 2.09440.8660-0.5000 2.61800.5000-0.8660 3.14160.0000 3.6652-0.5000-0.8660 4.1888-0.8660-0.5000 4.71240.0000 5.2360-0.86600.5000 5.7596-0.50000.8660 6.28320.00001.0000

3. 3 Graphing the Ordered Pairs Period = 2 π Maximum and minimum values

4. 4 Graphing on Calculator  Go to ♦Y= screen Enter function  Choose F2, zoom 7-Trig  Graph is plotted Tic marks are in units of π/2 Try Web Graphing Utility

5. 5 Amplitude  Defined as the absolute value of maximum or minimum of the function  Try graphing y = 2 cos x What is the amplitude  For y = a cos x or y = a sin x The amplitude is |a| amplitude = 1

6. 6 Period of a Trig Function (Recall slide from previous lesson)  The functions repeat themselves  The period is the smallest value, p for which f(x) = f(x + p)  For sin, cos, sec, csc The period is 2 π  For tan and ctn The period is π

7. 7 Period of a Trig Function  What happens for ?  Try graphing y = sin 3x What is the period?  Try y = cos 0.5x What is the period?  For Period = Same for cos, sec, csc

8. 8 Period of a Trig Function  For tangent Note amplitude is without bound Period is π  For Period = Predict the period for y = tan (1/3 x) Graph it and verify your prediction Predict the period for y = tan (1/3 x) Graph it and verify your prediction

9. 9 Assignment  Lesson 2.5  Page 177  Exercises 1 – 61 EOO also 63