Hprec7.1
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Transcript of Hprec7.1
7.1: Graphs of the Sine, Cosine & Tangent Functions
© 2008 Roy L. Gover(www.mrgover.com)
Learning Goals:
•Graph Trig functions
•Analyze and interpret Trig graphs
Example
Using a table of values, graph
siny tfor2 2t
23 2
202
3 22
Try This
Using a table of values, graph
cosy tfor2 2t
23 2
202
3 22
2
Solution
20
t
Example
Using your graphing calculator, graph ( ) cosg t ton the interval 3 ,2
Try This
On a sheet of paper, compare and contrast the graphs:siny t
cosy t
Example
sin t
Without using your graphing calculator, find all values of t for which is 1.
Try This
cos t
Without using your graphing calculator, find all values of tfor which
is 1.0 2t k
k=integer
ExampleWithout using your calculator, find all values of t between 0 and 2 for which
sin t
= 12
20
12
Try ThisWithout using your calculator, find all values of t between 0 and 2 for which
cos t= 1
2
5,
3 3t
Analysis
( ) cosf t tFor :
•What is the domain and range?
•What is the unit of measure for the t and axes?
( )f t
DefinitionThe Domain of a function is all possible values of the independent variable (t,x,θ)The Range of a function is all possible values of the dependent variable
, ( ), ( )y f t f
Analysis
( ) cosf t t( ) sinf t t
Compare and contrast the two graphs.
+1
-1
Try This
What is wrong with these statements:
3cos
2t
sin 2t
Try This
Graph the function :
( ) tanf x x
using your graphing calculator
Solution
( ) tanf x x
What is the domain and range?
What are Asymptotes and where do they occur?
Important IdeaAsymptotes occur at all points in the domain where the function is not defined.
(0,-1)
(-1,0) (1,0)
(0,1)
Important IdeaAsymptotes occur at all points in the domain where the function is not defined.
(0,-1)
(-1,0) (1,0)
(0,1)
Try This
Compare and contrast the graphs:
siny t
siny t
1
-1
Try This
Compare and contrast the graphs:
siny t
sin 1.5y t
2.5
1
ExampleFor what values of t on the interval 2 ,2 is:
( )f t• increasing• decreasing
( )f t
• ( ) 0f t 2 2
( ) cosf t t
Example
0 cos 1t
For what values of t on the interval 3 ,2 is:
3 2
( ) cosf t t
Example
3cos
2t
For what values of t on the interval 2 ,2 is:
2 2
( ) cosf t t
3
2
Example
3cos
2t
Name all, exact values of t for which
( ) cosf t t
3
2
Try This
1sin
2t
Name all, exact values of t for which
1
2
( ) sinf t t
26
t n
52
6t n
or
Lesson Close
Define:
•Domain
•Range