Download Chapter 6 – Graphs and Inverses of the Trigonometric Functions

Chapter 6 – Graphs and Inverses
of the Trigonometric Functions
6.1 Graphs of Trigonometric Functions
First as a class let’s graph y = sin x and y = cos x.
y = tan x
A function is periodic if for some number alpha, f ( x)  f ( x   ) for each x in domain of f.
The least positive value of alpha for which f ( x)  f ( x   ) is the period of the function.
Example: Use the graph of the cosine function to find the value of theta for which
cos  1
Example: Graph the sine curve in the interval 540    0
6.2 Amplitude, Period, and Phase Shift
What is and amplitude? Where can we find it in a function? And what does it tell us
about a function?
Ex: State the amplitude of the function y  3cos  . Graph y  3cos  and y  cos  on
the same set of axes. Compare the graphs.
What is the period of a function? How can it help us to graph a function? What affect does
the period have on the function?
Example: State the period of the function y  4sin . Then graph the function and y  sin 
on the same set of axes.
What is a phase shift? How does it affect the graphs?
Example: State the phase shift of the function y  tan   45  . Then graph the function and y
= tan x on the same axes.
Example: Find the possible equations of a cosine function with amplitude 3, period 90
degrees, and phase shift 45 degrees.
6.3 Graphing Trigonometric
Functions
Create rules for graphing and try some different examples.
6.4 Inverse Trigonometric
Functions
Find all positive values of x for which cos x 
sin(arcsin 0.4212)
2
cos  
2
3
2
 1 5 
tan  sin

13 

6.5 Principal Values of the Inverse
Trigonometric Functions
1
arccos  
2
1

sin  sin 1 1  cos 1 
2



sin 1  tan 
4

5
5

sin  arcsin  arc cot 
12
3
