Trigonometry Graphs www mathsrevision com Int 2 Graphs

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

Starter www. mathsrevision. com Int 2 created by Mr. Lafferty

Sine Graph www. mathsrevision. com Int 2 Learning Intention Success Criteria 1. To investigate graphs of the form y = a sin xo y = a cos xo y = tan xo created by Mr. Lafferty 1. Identify the key points for various graphs.

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

What effect does the number at the front have on the Int 2 graphs ? Sine Graph y = 2 sinxo y = 3 sinxo 3 www. mathsrevision. com y = sinxo y = 0. 5 sinxo y = -sinxo 2 1 0 90 o 180 o -1 -2 -3 created by Mr. Lafferty 270 o 360 o

Sine Graph 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

Sine Graph y = 4 sinxo y = sinxo Int 2 y = -6 sinxo 6 www. mathsrevision. com y = 5 sinxo 4 2 0 90 o 180 o -2 -4 -6 created by Mr. Lafferty 270 o 360 o

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

What effect does the number at the front have on the Int 2 graphs ? Cosine y = 2 cosx y = cosxo y = 3 cosxo 3 www. mathsrevision. com o y = 0. 5 cosxo y = -cosxo 2 1 0 90 o 180 o -1 -2 -3 created by Mr. Lafferty 270 o 360 o

Cosine Graph y = 4 cosx y = cosxo o Int 2 y = 6 cosxo www. mathsrevision. com 6 y = cosxo y = -cosxo 4 2 0 90 o 180 o -2 -4 -6 created by Mr. Lafferty 270 o 360 o

Key Features Tangent Graphs Zeros at 0 and 180 o www. mathsrevision. com Int 2 Key Features Domain is 0 to 180 o (repeats itself every 180 o) created by Mr. Lafferty

Tangent Graphs www. mathsrevision. com Int 2 created by Mr. Lafferty

Tangent Graph 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

Combination Graphs www. mathsrevision. com Int 2 Revision Booklet All questions created by Mr. Lafferty

Starter www. mathsrevision. com Int 2 created by Mr. Lafferty

Trig Graphs www. mathsrevision. com Int 2 Learning Intention Success Criteria 1. To investigate graphs of the form y = a sin bxo y = a cos bxo y = tan bxo created by Mr. Lafferty 1. Identify the key points for more complicated Trig graphs.

Period of a Function 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 360 o Let’s investigate the function y = sin bx created by Mr. Lafferty

What effect does the number in front of x have on the Int 2 graphs ? Sine Graph y = sin 2 xo y = sin 4 xo 3 www. mathsrevision. com y = sinxo y = sin 0. 5 xo 2 1 0 90 o 180 o -1 -2 -3 created by Mr. Lafferty 270 o 360 o

www. mathsrevision. com Int 2 Trigonometry Graphs y = a sin (bx) How many times it repeats itself in 360 o 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

What effect does the number at the front have on the Int 2 graphs ? Cosine y = cosx y = cos 2 xo y = cos 3 xo 3 www. mathsrevision. com o 2 1 0 90 o 180 o -1 -2 -3 created by Mr. Lafferty 270 o 360 o

www. mathsrevision. com Int 2 Trigonometry Graphs y = a cos (bx) How many times it repeats itself in 360 o 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

www. mathsrevision. com Int 2 Trigonometry Graphs y = a tan (bx) How many times it repeats itself in 180 o 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

Write down equations for graphs shown ? Trig Graph Combinations Int 2 y = 0. 5 sin 2 xo y = 2 sin 4 xo y = 3 sin 0. 5 xo www. mathsrevision. com 3 2 1 0 90 o 180 o -1 -2 -3 created by Mr. Lafferty 270 o 360 o

Write down equations for the graphs shown? Cosine Combinations Int 2 www. mathsrevision. com 3 y = 1. 5 cos 2 xo y = -2 cos 2 xo y = 0. 5 cos 4 xo 2 1 0 90 o 180 o -1 -2 -3 created by Mr. Lafferty 270 o 360 o

Combination Graphs www. mathsrevision. com Int 2 Revision Booklet All questions created by Mr. Lafferty

Starter www. mathsrevision. com Int 2 created by Mr. Lafferty

Phase Angle www. mathsrevision. com Int 2 Learning Intention Success Criteria 1. To explain what phase angle / phase shift is using knowledge from quadratics. 1. Understand the term phase angle / phase shift. 2. Read off the values for a and b for a graph of the form. y = a sin( x – c )o created by Mr. Lafferty

Sine Graph By how much do we have to move the standard sine curve so it fits on the Int 2 other sine curve? www. mathsrevision. com y = sin(x - 45)o 1 0 To the right “-” 45 o 90 o 180 o -1 created by Mr. Lafferty 270 o 360 o

Sine Graph By how much do we have to move the standard sine curve so it fits on the Int 2 other sine curve? www. mathsrevision. com y = sin(x + 60)o 1 To the left “+” 60 o -60 o 0 90 o 180 o -1 created by Mr. Lafferty 270 o 360 o

www. mathsrevision. com Int 2 Phase Angle 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

Cosine Graph By how much do we have to move the standard cosine curve so it fits on Int 2 the other cosine curve? www. mathsrevision. com y = cos(x - 70)o 1 0 To the right “-” 70 o o 90 o 160 180 o -1 created by Mr. Lafferty 270 o 360 o

Cosine Graph By how much do we have to move the standard cosine curve so it fits on Int 2 the other cosine curve? www. mathsrevision. com y = cos(x + 56)o 1 0 To the left “+” 56 o 34 o 90 o 180 o -1 created by Mr. Lafferty 270 o 360 o

Int 2 Summary of work So far www. mathsrevision. com 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

Sketch Graph Int 2 y = a cos (x – b) www. mathsrevision. com a =3 b =30 y = 2 cos (x - 30) created by Mr. Lafferty

Combination Graphs www. mathsrevision. com Int 2 Revision Booklet All questions created by Mr. Lafferty

Starter www. mathsrevision. com Int 2 created by Mr. Lafferty

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

Solving Trig Equations www. mathsrevision. com Int 2 Sin +ve All +ve 180 o - xo 1 2 3 4 created by Mr. Lafferty 180 o + xo 360 o - xo Tan +ve Cos +ve

Solving Trig Equations Graphically what a sin xo + b are = 0 we trying to solve Int 2 www. mathsrevision. com Example 1 : Solving the equation sin xo = 0. 5 in the range 0 o to 360 o sin xo = (0. 5) xo = sin-1(0. 5) xo = 30 o There is another solution 1 2 3 4 created by Mr. Lafferty xo = 150 o (180 o – 30 o = 150 o)

Solving Trig Equations Graphically what a sin xo + b are = 0 we trying to solve Int 2 www. mathsrevision. com Example 1 : Solving the equation 3 sin xo + 1= 0 in the range 0 o to 360 o sin xo = -1/3 Calculate first Quad value xo = 19. 5 o x = 180 o + 19. 5 o = 199. 5 o There is another solution 1 2 3 4 created by Mr. Lafferty ( 360 o - 19. 5 o = 340. 5 o)

Solving Trig Equations Graphically what a cos xo + b are = 0 we trying to solve Int 2 www. mathsrevision. com Example 1 : Solving the equation cos xo = 0. 625 in the range 0 o to 360 o cos xo = 0. 625 xo = cos -1 0. 625 xo = 51. 3 o There is another solution 1 2 3 4 created by Mr. Lafferty (360 o - 53. 1 o = 308. 7 o)

Solving Trig Equations Graphically what a tan xo + b are = 0 we trying to solve Int 2 www. mathsrevision. com Example 1 : Solving the equation tan xo = 2 in the range 0 o to 360 o tan xo = 2 xo = tan -1(2) xo = 63. 4 o There is another solution 1 2 3 4 created by Mr. Lafferty x = 180 o + 63. 4 o = 243. 4 o

Solving Trig Equations www. mathsrevision. com Int 2 Now try MIA Ex 6 First Column Only (page 249) created by Mr. Lafferty

Starter www. mathsrevision. com Int 2 created by Mr. Lafferty

Solving Trig Equations www. mathsrevision. com Int 2 Learning Intention Success Criteria 1. To explain some special trig relationships sin 2 xo + cos 2 xo = ? and tan xo and sin x cos x created by Mr. Lafferty 1. Know and learn the two special trig relationships. 2. Apply them to solve problems.

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

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

Solving Trig Equations www. mathsrevision. com Int 2 Now try MIA Ex 7 (page 252) created by Mr. Lafferty