Trigonometry Graphs www mathsrevision com Nat 5 Creation

Trigonometry Graphs www. mathsrevision. com Nat 5 Creation of BASIC Trig Graphs of the form y = a sin xo Graphs of the form y = a sin bxo + c Phase angle y = a sin(x + d) Exam Type Questions created by Mr. Lafferty

www. mathsrevision. com Nat 5 Trig Graphs Creation of a sine graph Sine Graph Creation of a cosine graph Cosine Graph Creation of a tan graph Tan Graph Let’s investigate created by Mr. Lafferty Graphs

Key Features Sine Graph Max value occurs at x = 90 Zeros (Root) at 0, 180 o and 360 o Nat 5 o www. mathsrevision. com Mini value occurs at x = 270 o Key Features (Period is every 360 o) Maximum value of 1 - AMPLITUDE Minimum value of -1 created by Mr. Lafferty

Cosine Graphs Zeros (Roots) at 90 and 270 Key Features o Max value occurs at x = 0 o and 360 o Nat 5 Minimum value occurs at x = 180 o www. mathsrevision. com o Key Features (Period is 360 o) Maximum value of 1 - AMPLITUDE Minimum value of -1 created by Mr. Lafferty

Key Features Tangent Graphs Zeros (Roots) at 0 and 180 o www. mathsrevision. com Nat 5 Key Features (Period is 180 o) created by Mr. Lafferty

Trig Graphs www. mathsrevision. com Nat 5 Work through N 5 TJ Ex 16. 1 , 16. 2 and 16. 3 (Page 157) created by Mr. Lafferty

Starter www. mathsrevision. com Nat 5 created by Mr. Lafferty

Sine & Cosine Graph www. mathsrevision. com Nat 5 Learning Intention Success Criteria 1. To investigate graphs of the form 1. Identify the key points for various trig graphs including Amplitude Period Roots. y = a sin xo y = a cos xo created by Mr. Lafferty

Key Features Sine Graph Max value at x = 90 Zeros at 0, 180 o and 360 o Nat 5 o www. mathsrevision. com Minimum value at x = 270 o Key Features (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 Nat 5 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 270 o 360 o -1 -2 -3 created by Mr. Lafferty Demo

Sine Graph www. mathsrevision. com Nat 5 y = a sin (x) For a > 1 stretches graph in the y-axis direction For 0 < 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 Nat 5 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 Nat 5 www. mathsrevision. com Minimum value at x = 180 o Key Features (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 Nat 5 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 270 o 360 o -1 -2 -3 created by Mr. Lafferty Demo

Cosine Graph y = 4 cosx y = cosxo o Nat 5 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

Trig Graphs www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 16. 4 (Page 161) created by Mr. Lafferty

Starter www. mathsrevision. com Nat 5 created by Mr. Lafferty

Trig Graphs www. mathsrevision. com Nat 5 Learning Intention Success Criteria 1. To investigate graphs of the form 1. Identify the key points for various trig graphs including Amplitude Period Roots. y = a sin bxo y = a cos bxo created by Mr. Lafferty

Period of a Function www. mathsrevision. com Nat 5 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 Nat 5 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 270 o 360 o -1 -2 -3 created by Mr. Lafferty Demo

www. mathsrevision. com Nat 5 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 0 < 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 Nat 5 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 Nat 5 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 0 < 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 Nat 5 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 0 < 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 Nat 5 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 270 o 360 o -1 -2 -3 created by Mr. Lafferty Demo

Write down equations for the graphs shown? Cosine Combinations Nat 5 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

Trig Graphs www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 16. 5 (Page 163) created by Mr. Lafferty

Starter www. mathsrevision. com Nat 5 created by Mr. Lafferty

y = asin(bx)o + c www. mathsrevision. com Nat 5 Learning Intention Success Criteria 1. We are learning how to sketch graphs of the type y = asin(bx)o + c 1. Identify and sketch the key points for various trig graphs including Amplitude Period Roots. y = acos(bx)o + c created by Mr. Lafferty

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

Write down the equations for the graphs shown? www. mathsrevision. com Higher DEMO Trig Graphsy = cos 2 x + 1 o o Combinationsy = -2 cos 2 x - 1 3 2 1 0 90 o 180 o -1 -2 -3 created by Mr. Lafferty 270 o 360 o

Trig Graphs www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 16. 6 (Page 165) created by Mr. Lafferty

Starter www. mathsrevision. com Nat 5 created by Mr. Lafferty

Phase Angle www. mathsrevision. com Nat 5 Learning Intention Success Criteria 1. To investigate graphs of the form y = asin(xo + d) 1. Identify and sketch the key points for trig graphs of the form y = asin(xo + d) y = acos(xo + d) created by Mr. Lafferty

Phase Angle www. mathsrevision. com By how much do we have to move the standard sine curve so it fits on the Nat 5 other sine curve? 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

Phase Angle www. mathsrevision. com By how much do we have to move the standard sine curve so it fits on the Nat 5 other sine curve? y = sin(x - 45)o 1 0 To the right “-” 45 o 90 o 180 o 270 o 360 o -1 created by Mr. Lafferty Demo

www. mathsrevision. com Nat 5 Phase Angle y = sin (x + d) Moves graph along x - axis For d > 0 moves graph to the left along x – axis For d < 0 moves graph to the right along x – axis created by Mr. Lafferty

Phase Angle www. mathsrevision. com By how much do we have to move the standard cosine curve so it fits on Nat 5 the other cosine curve? 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

Phase Angle www. mathsrevision. com By how much do we have to move the standard cosine curve so it fits on Nat 5 the other cosine curve? 1 0 y = cos(x + 56)o To the left “+” 56 o 34 o 90 o 180 o -1 created by Mr. Lafferty 270 o 360 o

Nat 5 Summary of work So far www. mathsrevision. com y = a sin (x + d) For a > 1 stretches graph in the y-axis direction For d > 0 moves graph to the left along x – axis For 0 < a < 1 compresses graph For d < 0 moves graph to in the y - axis direction the right along x – axis For a - negative flips graph in the x – axis. created by Mr. Lafferty

Phase Angle www. mathsrevision. com Nat 5 Now try N 5 TJ Ex 16. 7 (Page 168) created by Mr. Lafferty