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