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

2. Example
Using a
table of
values,
graph
siny t=
for
2 2tπ π− ≤ ≤
2π−
3 2π−
π−
2π−
0
2π
π
3 2π
2π

3. Try This
Using a
table of
values,
graph
cosy t=
for
2 2tπ π− ≤ ≤
2π−
3 2π−
π−
2π−
0
2π
π
3 2π
2π

4. 2π−
Solution
2π0
t

5. Example
Using your graphing
calculator, graph ( ) cosg t t=
on the interval [ ]3 ,2π π−

6. Try ThisOn a
sheet of
paper,
compare
and
contrast
the
graphs:siny t=
cosy t=

7. Example
cosy t=
1
-1
0
Animate

8. Example
sint
Without using your graphing
calculator, find all values of
t for which is 1.

9. Try This
cost
Without
using your
graphing
calculator,
find all
values of t
for which
is 1.
0 2t kπ= +
k=integer

10. ExampleWithout
using your
calculator,
find all
values of t
between 0
and 2 for
which
π
sint
= 1
2
2π0
1
2

11. Try This
Without using your
calculator, find all values
of t between 0 and 2 for
which
π
cost= 1
2
5
,
3 3
t
π π
=

12. Analysis
( ) cosf t t=For :
•What is the domain and
range?
•What is the unit of measure
for the t and axes?( )f t

13. Definition
The 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 θ

14. Analysis
( ) cosf t t=( ) sinf t t=
Compare and contrast
the two graphs.
+1
-1

15. Try This
What is
wrong with
these
statements: 3
cos
2
t = −
sin 2t =

16. Try This
Graph the function :
( ) tanf x x=
using your graphing
calculator

17. Solution
( ) tanf x x=
What is the
domain and
range?
What are
Asymptotes
and where
do they
occur?

18. Important Idea
Asymptotes
occur at all
points in the
domain
where the
function is
not defined.
(0,-1)
(-1,0) (1,0)
(0,1)

19. Important Idea
Asymptotes
occur at all
points in the
domain
where the
function is
not defined.
(0,-1)
(-1,0) (1,0)
(0,1)

20. Try ThisCompare
and
contrast
the
graphs:
siny t= −
siny t=
1
-1

21. Try ThisCompare
and
contrast
the
graphs:
siny t=
sin 1.5y t= +
2.5
1

22. Example
For what
values of t on
the interval
[ ]2 ,2π π− is:
( )f t• increasing
• decreasing( )f t
• ( ) 0f t < 2π− 2π
( ) cosf t t=

23. Example
0 cos 1t< <
For what
values of t on
the interval
[ ]3 ,2π π− is:
3π− 2π
( ) cosf t t=

24. Example
3
cos
2
t = −
For what
values of t on
the interval
[ ]2 ,2π π− is:
2π− 2π
( ) cosf t t=
3
2
−

25. Example
3
cos
2
t = −
Name all,
exact
values of t
for which
( ) cosf t t=
3
2
−

26. Try This
1
sin
2
t =
Name all,
exact
values of t
for which
1
2
( ) sinf t t=
2
6
t n
π
π= +
5
2
6
t n
π
π= +
or

27. Lesson Close
Define:
•Domain
•Range