Graphs of Sine and Cosine Functions Lesson 2.5. 2 Ordered Pairs  Consider the values for x and y in the table to the right  Note Period = 2 π Maximum.

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Graphs of Sine and Cosine Functions Lesson 2.5

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

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