Download presentation

Presentation is loading. Please wait.

Published byLondon Hewes Modified over 2 years ago

1
**Trigonometry Graphs www.mathsrevision.com**

Int 2 Graphs of the form y = a sin xo Graphs of the form y = a sin bxo Phase angle Solving Trig Equations Special trig relationships created by Mr. Lafferty

2
Starter Int 2 created by Mr. Lafferty

3
**Sine Graph www.mathsrevision.com Int 2 Learning Intention**

Success Criteria To investigate graphs of the form y = a sin xo y = a cos xo y = tan xo Identify the key points for various graphs. created by Mr. Lafferty

4
**Sine Graph www.mathsrevision.com Key Features**

Zeros at 0, 180o and 360o Max value at x = 90o Int 2 Minimum value at x = 270o Key Features Domain is 0 to 360o (repeats itself every 360o) Maximum value of 1 Minimum value of -1 created by Mr. Lafferty

5
**What effect does the number at the front have on the graphs ?**

y = sinxo y = 2sinxo y = 3sinxo y = 0.5sinxo y = -sinxo Sine Graph Int 2 3 2 1 90o 180o 270o 360o -1 -2 -3 created by Mr. Lafferty

6
**Sine Graph y = a sin (x) www.mathsrevision.com**

Int 2 y = a sin (x) For a > 1 stretches graph in the y-axis direction For a < 1 compresses graph in the y - axis direction For a - negative flips graph in the x – axis. created by Mr. Lafferty

7
**Sine Graph www.mathsrevision.com 6 4 2 -2 -4 -6 y = 5sinxo y = 4sinxo**

Int 2 6 4 2 90o 180o 270o 360o -2 -4 -6 created by Mr. Lafferty

8
**Cosine Graphs www.mathsrevision.com Key Features Zeros at 90o and 270o**

Max value at x = 0o and 360o Int 2 Minimum value at x = 180o Key Features Domain is 0 to 360o (repeats itself every 360o) Maximum value of 1 Minimum value of -1 created by Mr. Lafferty

9
**What effect does the number at the front have on the graphs ?**

y = cosxo y = 2cosxo y = 3cosxo y = 0.5cosxo y = -cosxo Cosine Int 2 3 2 1 90o 180o 270o 360o -1 -2 -3 created by Mr. Lafferty

10
**Cosine Graph www.mathsrevision.com 6 4 2 -2 -4 -6 y = cosxo y = 4cosxo**

Int 2 6 4 2 90o 180o 270o 360o -2 -4 -6 created by Mr. Lafferty

11
**Tangent Graphs www.mathsrevision.com Key Features Zeros at 0 and 180o**

Int 2 Key Features Domain is 0 to 180o (repeats itself every 180o) created by Mr. Lafferty

12
Tangent Graphs Int 2 created by Mr. Lafferty

13
**Tangent Graph y = a tan (x) www.mathsrevision.com**

Int 2 y = a tan (x) For a > 1 stretches graph in the y-axis direction For a < 1 compresses graph in the y - axis direction For a - negative flips graph in the x – axis. created by Mr. Lafferty

14
**Combination Graphs Revision Booklet All questions**

Int 2 Revision Booklet All questions created by Mr. Lafferty

15
Starter Int 2 created by Mr. Lafferty

16
**Trig Graphs www.mathsrevision.com Int 2 Learning Intention**

Success Criteria To investigate graphs of the form y = a sin bxo y = a cos bxo y = tan bxo Identify the key points for more complicated Trig graphs. created by Mr. Lafferty

17
**Period of a Function y = sin bx www.mathsrevision.com**

Int 2 When a pattern repeats itself over and over, it is said to be periodic. Sine function has a period of 360o Let’s investigate the function y = sin bx created by Mr. Lafferty

18
**What effect does the number in front of x have on the graphs ?**

y = sinxo y = sin2xo y = sin4xo y = sin0.5xo Sine Graph Int 2 3 2 1 90o 180o 270o 360o -1 -2 -3 created by Mr. Lafferty

19
**Trigonometry Graphs y = a sin (bx) www.mathsrevision.com**

Int 2 y = a sin (bx) How many times it repeats itself in 360o For a > 1 stretches graph in the y-axis direction For a < 1 compresses graph in the y - axis direction For a - negative flips graph in the x – axis. created by Mr. Lafferty

20
**What effect does the number at the front have on the graphs ?**

Cosine y = cosxo y = cos2xo y = cos3xo Int 2 3 2 1 90o 180o 270o 360o -1 -2 -3 created by Mr. Lafferty

21
**Trigonometry Graphs y = a cos (bx) www.mathsrevision.com**

Int 2 y = a cos (bx) How many times it repeats itself in 360o For a > 1 stretches graph in the y-axis direction For a < 1 compresses graph in the y - axis direction For a - negative flips graph in the x – axis. created by Mr. Lafferty

22
**Trigonometry Graphs y = a tan (bx) www.mathsrevision.com**

Int 2 y = a tan (bx) How many times it repeats itself in 180o For a > 1 stretches graph in the y-axis direction For a < 1 compresses graph in the y - axis direction For a - negative flips graph in the x – axis. created by Mr. Lafferty

23
**Write down equations for graphs shown ?**

y = 0.5sin2xo y = 2sin4xo y = 3sin0.5xo Trig Graph Combinations Int 2 3 2 1 90o 180o 270o 360o -1 -2 -3 created by Mr. Lafferty

24
**Write down equations for the graphs shown?**

y = 1.5cos2xo y = -2cos2xo y = 0.5cos4xo Cosine Combinations Int 2 3 2 1 90o 180o 270o 360o -1 -2 -3 created by Mr. Lafferty

25
**Combination Graphs Revision Booklet All questions**

Int 2 Revision Booklet All questions created by Mr. Lafferty

26
Starter Int 2 created by Mr. Lafferty

27
**Phase Angle www.mathsrevision.com Int 2 Learning Intention**

Success Criteria To explain what phase angle / phase shift is using knowledge from quadratics. Understand the term phase angle / phase shift. Read off the values for a and b for a graph of the form. y = a sin( x – c )o created by Mr. Lafferty

28
**Sine Graph www.mathsrevision.com y = sin(x - 45)o 1 To the right “-”**

By how much do we have to move the standard sine curve so it fits on the other sine curve? Sine Graph Int 2 y = sin(x - 45)o 1 To the right “-” 45o 45o 90o 180o 270o 360o -1 created by Mr. Lafferty

29
**Sine Graph www.mathsrevision.com y = sin(x + 60)o 1 To the left “+” -1**

By how much do we have to move the standard sine curve so it fits on the other sine curve? Sine Graph Int 2 y = sin(x + 60)o 1 To the left “+” 60o -60o 90o 180o 270o 360o -1 created by Mr. Lafferty

30
**Phase Angle y = sin (x - c) www.mathsrevision.com Moves graph**

Int 2 y = sin (x - c) Moves graph along x - axis For c > 0 moves graph to the right along x – axis For c < 0 moves graph to the left along x – axis created by Mr. Lafferty

31
**Cosine Graph www.mathsrevision.com y = cos(x - 70)o 1 To the right “-”**

By how much do we have to move the standard cosine curve so it fits on the other cosine curve? Cosine Graph Int 2 y = cos(x - 70)o 1 To the right “-” 70o 90o 160o 180o 270o 360o -1 created by Mr. Lafferty

32
**Cosine Graph www.mathsrevision.com y = cos(x + 56)o 1 To the left “+”**

By how much do we have to move the standard cosine curve so it fits on the other cosine curve? Cosine Graph Int 2 y = cos(x + 56)o 1 To the left “+” 56o 34o 90o 180o 270o 360o -1 created by Mr. Lafferty

33
**y = a sin (x - b) Summary of work So far www.mathsrevision.com**

Int 2 y = a sin (x - b) For a > 1 stretches graph in the y-axis direction For b > 0 moves graph to the right along x – axis For a < 1 compresses graph in the y - axis direction For b < 0 moves graph to the left along x – axis For a - negative flips graph in the x – axis. created by Mr. Lafferty

34
**Sketch Graph www.mathsrevision.com y = a cos (x – b) a =3 b =30**

Int 2 a =3 b =30 y = 2 cos (x - 30) created by Mr. Lafferty

35
**Combination Graphs Revision Booklet All questions**

Int 2 Revision Booklet All questions created by Mr. Lafferty

36
Starter Int 2 created by Mr. Lafferty

37
**Solving Trig Equations**

Int 2 Learning Intention Success Criteria To explain how to solve trig equations of the form a sin xo + 1 = 0 Use the rule for solving any ‘ normal ‘ equation Realise that there are many solutions to trig equations depending on domain. created by Mr. Lafferty

38
**Solving Trig Equations**

Int 2 1 2 3 4 Sin +ve All +ve 180o - xo 180o + xo 360o - xo Tan +ve Cos +ve created by Mr. Lafferty

39
**Solving Trig Equations**

Graphically what are we trying to solve a sin xo + b = 0 Int 2 Example 1 : Solving the equation sin xo = 0.5 in the range 0o to 360o sin xo = (0.5) 1 2 3 4 xo = sin-1(0.5) xo = 30o There is another solution xo = 150o (180o – 30o = 150o) created by Mr. Lafferty

40
**Solving Trig Equations**

Graphically what are we trying to solve a sin xo + b = 0 Int 2 Example 1 : Solving the equation 3sin xo + 1= 0 in the range 0o to 360o 1 2 3 4 sin xo = -1/3 Calculate first Quad value xo = 19.5o x = 180o o = 199.5o There is another solution ( 360o o = 340.5o) created by Mr. Lafferty

41
**Solving Trig Equations**

Graphically what are we trying to solve a cos xo + b = 0 Int 2 Example 1 : Solving the equation cos xo = in the range 0o to 360o 1 2 3 4 cos xo = 0.625 xo = cos xo = 51.3o There is another solution (360o o = 308.7o) created by Mr. Lafferty

42
**Solving Trig Equations**

Graphically what are we trying to solve a tan xo + b = 0 Int 2 Example 1 : Solving the equation tan xo = 2 in the range 0o to 360o 1 2 3 4 tan xo = 2 xo = tan -1(2) xo = 63.4o There is another solution x = 180o o = 243.4o created by Mr. Lafferty

43
**Solving Trig Equations**

Int 2 Now try MIA Ex6 First Column Only (page 249) created by Mr. Lafferty

44
Starter Int 2 created by Mr. Lafferty

45
**Solving Trig Equations**

Int 2 Learning Intention Success Criteria To explain some special trig relationships sin 2 xo + cos 2 xo = ? and tan xo and sin x cos x Know and learn the two special trig relationships. Apply them to solve problems. created by Mr. Lafferty

46
**Solving Trig Equations**

Int 2 Lets investigate sin 2xo + cos 2 xo = ? Calculate value for x = 10, 20, 50, 250 sin 2xo + cos 2 xo = 1 Learn ! created by Mr. Lafferty

47
**Solving Trig Equations**

Int 2 Lets investigate sin xo cos xo tan xo and Calculate value for x = 10, 20, 50, 250 sin xo cos xo tan xo = Learn ! created by Mr. Lafferty

48
**Solving Trig Equations**

Int 2 Now try MIA Ex7 (page 252) created by Mr. Lafferty

Similar presentations

OK

Lesson 47 – Trigonometric Functions Math 2 Honors - Santowski 2/12/2016Math 2 Honors - Santowski1.

Lesson 47 – Trigonometric Functions Math 2 Honors - Santowski 2/12/2016Math 2 Honors - Santowski1.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on history of olympics video Ppt on mid day meal Ppt on thermal conductivity of insulating powder coating Ppt on workplace etiquette powerpoint presentation Free ppt on geothermal energy Ppt on bluetooth energy meter Ppt on indian herbs and spices Ppt on media in hindi Ppt on recycling and reuse of building waste in construction Ppt on tax management system project