More: www.PinoyBIX.org Lesson Objectives: Able to plot the different Trigonometric Graphs Graph of Tangent Function (y = f(x) = tanx) Graph of Cotangent Function (y = f(x) = cotx) Graph of Secant Function (y = f(x) = secx) Graph of Cosecant Function (y = f(x) = cscx) Define the Maximum and Minimum value in a graph Generalized Trigonometric Functions Graphs of y = sinbx Graphs of y = sin(bx + c) Could find the Period of Trigonometric Functions Could find the Amplitude of Trigonometric Functions Variations in the Trigonometric Functions

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Presents:
GRAPHS OF OTHER TRIG FUNCTIONS
credit: Shawna Haider

2. GRAPHS OF OTHER
TRIG FUNCTIONS
  xxf tan   xxf cot
  xxf sec   xxf cosec

3. 6


We are interested in the graph of y = f(x) = tan x
Start with a "t" chart and let's choose values from our unit
circle and find the tangent values. Tangent has a period
of  so it will repeat every .
x y = tan x
3


2

 undefined
73.13 
4

 1
6

 58.0
3
3

x
y
2


3


2

3

6

would mean there is
a vertical asymptote
here

4. 6


y = tan xLet's choose more values.
x y = tan x
6

0 0
73.13 
4

1
3

58.0
3
3

x
y
2


3


2

3

6

would mean there is a
vertical asymptote here
2

undefined
Since we went from we have one complete period
2
to
2



5. Let's see what the graph would look like for y = tan x
for 3 complete periods.
The vertical lines
are not part of
the graph but are
the asymptotes.
If you use your
graphing
calculator it will
probably put
those in as well
as showing the
graph.

6. Transformations apply as usual. Let’s try one.







4
tan2

xy
reflect about x-axis
right /4
up 2
xy tan
xy tan 






4
tan

xy







4
tan2

xy

7. Since the period of tangent is ,
the period of tan x is:


T
xy 2tan The period would be /2
y = tan x
y = tan 2x

8. 3


6


What about the graph of y = f(x) = cot x?
This would be the reciprocal of tangent so let's take our
tangent values and "flip" them over.
x tan x y = cot x
3


2

 undefined
3
4

 1
6


3
1

x
y
2


2

3

6

0
58.0
3
1

1
73.13 

9. 3


6


x tan x y = cot x
6

0 0
3
4

1
3

3
1
x
y
2


2

3

6

undefined
58.0
3
1

1
73.13 
y = cot xLet's choose more values.
2

undefined 0
We need to see
more than one
period to get a
good picture of
this.

10. y = cot x
Again the vertical lines are
not part of the graph but
are the asymptotes.
Let's look at the tangent graph
again to compare these.
Notice vertical
asymptotes of one are
zeros of the other.
y = tan x

11. For the graph of y = f(x) = cosec x we'll take the
reciprocals of the sine values.
x sin x y = cosec x
6

0 0
2
1
2

1
6
5
When we graph these rather than plot points
after we see this, we'll use the sine graph as a
sketching aid and then get the cosecant graph.
x
y
1
- 1
undefined
2
1
2
1
2

12. y = f(x) = cosec xchoose more values
x sin x y = cosec x
6
7
 0
2
1

2
3
1
6
11
2
1

We'll use the sine graph as the sketching aid.
x
y
1
- 1
2 0
6

 2
undefined
2
1
2
undefined
When the sine
is 0 the
cosecant will
have an
asymptote.

13. Again the vertical lines are not part of the graph but are where
the cosecant is undefined (which is where the sine was 0
although this graphing program seemed to draw them a little to
the right. They should cross the x-axis where the sine is 0)
Let's add in the
graph of the sine
function so you
can see how if
you graph it, you
can then easily
use it to graph
the cosecant.
Let's look over a few periods at the graph of y = cosec x

14. For the graph of y = f(x) = sec x we'll take the
reciprocal of the cosine values.
x cos x y = sec x
3

0 1
2
1
2

0
3
2
2
1

x
y
1
- 1 6

1
2
undefined
2

15. y = f(x) = sec x
Choose more values.
x cos x y = sec x
3
4
 1
2
1

2
3
0
3
5
2
1
Again the cosine graph will help graph the secant graph.
x
y
1
- 1 6

2 1
1
2
undefined
2
1

16. Again the vertical lines are not part of the graph but are where
the secant is undefined (which is where the cosine was 0)
Let's look over a few periods at the graph of y =sec x
Let's add in the graph of the cosine function so you can
see how if you graph it, you can then easily use it to
graph the secant.

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