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**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

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Starter Int 2 created by Mr. Lafferty

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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Tangent Graphs Int 2 created by Mr. Lafferty

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**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

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**Combination Graphs Revision Booklet All questions**

Int 2 Revision Booklet All questions created by Mr. Lafferty

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Starter Int 2 created by Mr. Lafferty

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**Combination Graphs Revision Booklet All questions**

Int 2 Revision Booklet All questions created by Mr. Lafferty

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Starter Int 2 created by Mr. Lafferty

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**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

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**Combination Graphs Revision Booklet All questions**

Int 2 Revision Booklet All questions created by Mr. Lafferty

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Starter Int 2 created by Mr. Lafferty

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**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

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**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

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**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

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**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

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**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

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**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

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**Solving Trig Equations**

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

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Starter Int 2 created by Mr. Lafferty

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**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

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**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

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**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

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**Solving Trig Equations**

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

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Graphs of the form y = a sin x o Nat 5 Graphs of the form y = a sin bx o Phase angle Solving Trig Equations Special trig relationships Trigonometric Functions.

Graphs of the form y = a sin x o Nat 5 Graphs of the form y = a sin bx o Phase angle Solving Trig Equations Special trig relationships Trigonometric Functions.

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