6.4 : Graphs of Trigonometric Functions

[Pages:41]6.4 : Graphs of Trigonometric Functions

In this section, we will 1. revisit previous sections for important concepts 2. graph the basic trig. functions (based on the definitions from prev. sections) 3. define periodicity of a graph and other properties (e.g., amplitudes) 4. graph transformed trig. functions

Definition of trig functions and the ratios of the sides

Unit circle definition

x = cos , y = sin

Example

1)

Identify

the

corresponding

(x, y )

on

the

U.C.

if

=

6

Example

2)

Find

(x, y )

if

=

11 6

Fill in the blanks

The shape of cos t for t [0, 2)

For the graph of cos t, simply follow the x coordinates of the points below on the U.C. as t increases from 0 to 2.

Characteristics of f (t) = cos t

Domain : Range : Minimum : Maximum : Zeros :

The shape of sin t for t [0, 2)

For the graph of sin t, simply follow the y coordinates of the points below on the U.C. as t increases from 0 to 2.

Characteristics of f (t) = sin t

Domain : Range : Minimum : Maximum : Zeros :

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