Unit 5

1
Unit 5 Graphs of the other Trigonometric
Functions

• Tangent and Cotangent

Warm Up 1-9 on the trig graphs review page done
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.
2
In this section, you will learn to
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• Sketch the graphs of tangent and cotangent
  functions (Thursday/Friday)
• Sketch the graphs of secant and cosecant
  functions (Monday/Tuesday)

3
The graph of the tangent curve
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.
4
The graph of the tangent curve
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

5
The graph of the cotangent curve
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.
6
The graph of the cotangent curve
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

7

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• Question Is there an amplitude for a tangent or
  a cotangent function? Why or why not?
• No amplitude, since the two curves extend
  infinitely in both directions.

8
Period of Tangent and Cotangent Functions
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

THIS IS DIFFERENT
9
Asymptotes of the tangent graph
function
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• Where do you think you need to set the left and
  right endpoints for a tangent graph below?

10
Asymptotes of the tangent graph
function
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• Asymptotes for a tangent function can be found
• by solving for the two equations

11
Find the asymptotes of
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.
12
Find the asymptotes of
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.
13
Asymptotes of the cotangent graph
function
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• Where do you think you need to set the left and
  right endpoints for a cotangent graph below?

14
Asymptotes of the cotangent graph
function
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• Asymptotes for a cotangent function can be found
• by solving for the two equations

15
Find the asymptotes of
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.
16
Find the asymptotes of
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.
17
Reflection
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• If a is positive, then there is no reflection
  about the x-axis.
• If a is negative, then there is a reflection
  about the x-axis.

18

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

19

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

20

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

21

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

22
Effects of a on the tangent and cotangent
graphs

23
Effects of a on the tangent and cotangent graphs
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• a) If a gt 1, then the graph rises faster.
• b) If 0lt a lt 1, then the graph rises slower.
  

24
Effects of c on the tangent and cotangent
graphs
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

25
Horizontal Translation or Phase Shift
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• The constant c determines the phase shift of
  the graph.
• Phase Shift - c/b (or c/b)
• a) If c is positive, then the shift is toward
  the left.
• b) If c is negative, then the shift is toward
  the right.

26
Effects of d on the tangent and cotangent
graphs
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

27
Vertical Translation
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• The constant d determines the vertical
• translation of the graph.
• a) If d is positive, then the vertical shift is
  upward.
• b) If d is negative, then the vertical shift is
  downward.

28
Find the amplitude, period, reflections,
horizontal shift, vertical shift, endpoints and
sketch the graph.
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.
29
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• a) Amplitude
• b) Period
• c) Horizontal Translation
• d) Vertical Shift
• e) Reflection

30
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• e) Endpoints
• Verify distance with the period

31
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.
32
The graph of the secant curve
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

33
The graph of the secant curve
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

34
The graph of the cosecant curve
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

35
The graph of the cosecant curve
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

36

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• Is there an amplitude for a secant or a cosecant
  function? Why or why not?

37

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• Period is
• The horizontal translation, vertical translation,
  and reflection all stay the same.
• It is best to sketch the cosecant and secant
  graph by first graphing the reciprocal functions
  of sine and cosine.

38
Find the amplitude, period, reflections,
horizontal shift, vertical shift, endpoints and
sketch the graph.
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.
39
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• a) Amplitude
• b) Period
• c) Horizontal Translation
• d) Vertical Shift
• e) Reflection

40
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• e) Endpoints
• Verify distance with the period

41
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.
42

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

43

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

44

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

45

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

46

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

47

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

48

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

49

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

50

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

51

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.
52

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

53

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.
54
Reflection
MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

• If a is positive, then there is no reflection
  about the x-axis.
• If a is negative, then there is a reflection
  about the x-axis.
• If b is positive, then there is no reflection
  about the y-axis.
• If b is negative, then there is a reflection
  about the y-axis.

55

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

56

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

57

MM4A3. Students will investigate and use the
graphs of the six trigonometric functions. c.
Graph transformations of trigonometric functions
including changing period, amplitude, phase
shift, and vertical shift.

58
HOMEWORK

• Graphing Trig Functions
• Kuta
• Trig graphs review page 1 and 2