1. Trigonometry GraphsS4 Credit Exact values for Sin Cos and Tanwww.mathsrevision.com Angles greater than 90o Graphs of the form y = a sin xo Graphs of the form y = a sin bxo Graphs of the form y = a sin bxo + c Solving Trig Equations Special trig relationships created by Mr. Lafferty

2. Starter QuestionsS4 Credit 1. Factorise x2 - 36 www.mathsrevision.com 2. A car depreciates at 20% each year.How much is it worth after 1 year if it cost15 000 initially. 3. What is sin30o as a fraction. 23 Mar 2013Created by Mr Lafferty Maths Dept 3. Exact ValuesS4 Credit Learning Intention Success Criteria www.mathsrevision.com1. To build on basic1. Recognise basic triangles and trigonometry values.exact values for sin, cos and tan 30o, 45o, 60o .2. Calculate exact values for problems. 23 Mar 2013Created by Mr Lafferty Maths Dept 4. Exact ValuesS4 Credit Some special values of Sin, Cos and Tan are useful left as fractions, We call these exact values www.mathsrevision.com 60 30 2 2 236060 60 2 1 This triangle will provide exact values forsin, cos and tan 30 and 60 5. Exact ValuesS4 Credit x 0 30 45 60 90 www.mathsrevision.com3 Sin x 0 213 Cos x1 2 01 Tan x 0 33 6. Exact ValuesS4 Credit Consider the square with sides 1 unit www.mathsrevision.com 4511 2 45 1 1We are now in a position to calculate exact values for sin, cos and tan of 45o 7. Exact ValuesS5 Int2 x 0 30 45 60 90 www.mathsrevision.com 13 Sin x 0 2213 1 Cos x1 22 01 Tan x 0 3 13 8. Exact ValuesS5 Int2 www.mathsrevision.com Now try Ex 2.1 Ch11 (page 220) 23 Mar 2013Created by Mr Lafferty Maths Dept 9. Starter QuestionsS4 credit 1. True or false 2 + 3 7 = 35 www.mathsrevision.com 2. A house increases by 3% each year.How much is it worth after 1 years if it cost40 000 initially. 3. What is the exact value of sin 45o. 23 Mar 2013 Created by Mr Lafferty Maths Dept 10. Angles Greater than 90oS4 credit Learning Intention Success Criteria www.mathsrevision.com1. Introduce definition of1. Find values of sine, cosine sine, cosine and tangentand tangent over the range 0o over 360o using triangles to 360o. with the unity circle. 2. Recognise the symmetry andequal values for sine, cosineand tangent. 23 Mar 2013Created by Mr. Lafferty Maths Dept. 11. ryAngles Greater than 90o xS4 credit We will now use a new definition to cater for ALL angles. www.mathsrevision.comNew Definitions y-axis y sin A = yP(x,y) rr xAcos A = r Oo x x-axis y tan A = xMar 23, 2013www.mathsrevision.com 11 12. TrigonometryS4 creditExample Angles over 900 The radius line is 2cm. (1.2, 1.6) The point (1.2, 1.6). www.mathsrevision.com Find sin cos and tan for the angle. 1.6Check answer sin 53o = = 0.802with calculator1.2 cos 53 = o= 0.60 2 tan 53 = o1.6= 1.33 53o23 Mar 2013 1.2Created by Mr Lafferty Maths Dept 13. TrigonometryS4 creditExample 1Angles over 900 The radius line is 2cm.Check answer The point (-1.8, 0.8). with calculator www.mathsrevision.com Find sin cos and tan for the angle. (-1.8, 0.8) 0.8 sin127o = = 0.402 127o1.8 cos127 =o = 0.90 2 0.8tan127 = o= 0.44 23 Mar 2013 1.8 Created by Mr Lafferty Maths Dept 14. TrigonometrySummary ofresultsS4 creditExample All Quadrants Calculate the ration for sin cos and tan for the angle values below.90o www.mathsrevision.com 30o210o 45o225oSin +ve All +ve 60o240o 180o - xoxo 120o 300o0o 180o 135o 315o180o + xo 360o - xo 150o 330oTan +ve Cos +veSin x Cos xTan x23 Mar 2013 Created by Mr Lafferty Maths Dept270o 15. What Goes In The Box ?S4 credit Write down the equivalent values of the following in term of the first quadrant (between 0o and 90o): www.mathsrevision.com1) Sin 135osin 45 o 1) Sin 300o- sin 60o2) Cos 150o-cos 45o 2) Cos 360o cos 0o3) Tan 135 o -tan 45o 3) Tan 330 o - tan 30o4) Sin 225 o -sin 45o 4) Sin 380 osin 20o -cos 90o- cos 80o5) Cos 270o 5) Cos 460o 16. TrigonometryS4 credit Angles over 900 www.mathsrevision.com Now try MIA Ch11 Ex3.1 Ch11 (page 222) 23 Mar 2013Created by Mr Lafferty Maths Dept 17. StarterS4 Credit1. True or falsewww.mathsrevision.com 2x +7x+6 = ( 2x + 3)(x + 2) 22. A TV is reduced by 20% to 200. What was the original price.Q3. Solve (2x-1)(x-1) = 0 created by Mr. Lafferty 18. Sine GraphS4 CreditLearning Intention Success Criteriawww.mathsrevision.com1. To investigate graphs of 1. Identify the key points the formfor various graphs. y = a sin xo y = a cos xoy = tan xocreated by Mr. Lafferty 19. Key Features Sine Graph value at x = 90MaxZeros at 0, 180o and 360ooS4 Credit Minimum value at x = 270owww.mathsrevision.com Key Features Domain is 0 to 360o(repeats itself every 360o) Maximum value of 1 Minimum value of -1created by Mr. Lafferty 20. What effecty = sinxo does the numberat the frontSine Graphy = 2sinxo have on theS4 Credit graphs ?y = 3sinxo 3 y = 0.5sinxoy = -sinxo www.mathsrevision.com 21 090o180o270o 360o -1What effect -2 does thenegative sign have on the -3 graphs ? by Mr. Laffertycreated 21. Sine GraphS4 Credity = a sin (x)www.mathsrevision.comFor a > 1 stretches graph in the y-axis directionFor a < 1 compresses graph in the y - axis directionFor a - negative flips graph in the x axis. created by Mr. Lafferty 22. y = 5sinxo Sine Graph y = 4sinx o y = sinxoS4 Credit6y = -6sinxowww.mathsrevision.com4 20 90o 180o270o 360o-2-4-6 created by Mr. Lafferty 23. Cosine Graphsat 90 and 270 Key Features Zeroso oMax value at x = 0o and 360oS4 CreditMinimum value at x = 180owww.mathsrevision.com Key Features Domain is 0 to 360o(repeats itself every 360o) Maximum value of 1 Minimum value of -1created by Mr. Lafferty 24. What effect y = cosxo does the numberat the front Cosine 2cosxy= o have on theS4 Credit graphs ?y = 3cosxo 3y = 0.5cosxoy = -cosxo www.mathsrevision.com 21 090o 180o 270o 360o -1 -2 -3 created by Mr. Lafferty 25. y = 2cosxo Cosine Graph y = 4cosxoS4 Credit y = 6cosxo6 y = 0.5cosxoy = -cosxowww.mathsrevision.com4 2090o 180o270o 360o-2-4-6created by Mr. Lafferty 26. Key Features Tangent Graphs Zeros at 0 and 180oS4 Creditwww.mathsrevision.com Key Features Domain is 0 to 180o(repeats itself every 180o)created by Mr. Lafferty 27. Tangent GraphsS4 Creditwww.mathsrevision.com created by Mr. Lafferty 28. Tangent GraphS4 Credity = a tan (x)www.mathsrevision.comFor a > 1 stretches graph in the y-axis directionFor a < 1 compresses graph in the y - axis directionFor a - negative flips graph in the x axis. created by Mr. Lafferty 29. Period of a FunctionS4 CreditWhen a pattern repeats itself over and over,it is said to be periodic.www.mathsrevision.comSine function has a period of 360o Lets investigate the functiony = sin bxcreated by Mr. Lafferty 30. What effect does the numberin front of x Sine Graphy = sinxo have on they = sin2xoS4 Credit graphs ?y = sin4xo 3 y = sin0.5xo www.mathsrevision.com 21 0 90o 180o270o 360o -1 -2 -3created by Mr. Lafferty 31. Trigonometry GraphsS4 Credity = a sin (bx)www.mathsrevision.com How many timesit repeatsitself in 360oFor a > 1 stretches graph in the y-axis directionFor a < 1 compresses graph in the y - axis directionFor a - negative flips graph in the x axis. created by Mr. Lafferty 32. Cosinecosxy= o y = cos2xoS4 Credit y = cos3xo3www.mathsrevision.com2 10 90o 180o270o 360o-1-2-3 created by Mr. Lafferty 33. Trigonometry GraphsS4 Credity = a cos (bx)www.mathsrevision.com How many timesit repeatsitself in 360oFor a > 1 stretches graph in the y-axis directionFor a < 1 compresses graph in the y - axis directionFor a - negative flips graph in the x axis. created by Mr. Lafferty 34. Trigonometry GraphsS4 Credity = a tan (bx)www.mathsrevision.com How many timesit repeatsitself in 180oFor a > 1 stretches graph in the y-axis directionFor a < 1 compresses graph in the y - axis directionFor a - negative flips graph in the x axis. created by Mr. Lafferty 35. Write down theequations for the graphs shown ? Trig Graph y = 0.5sin2xo y = 2sin4xoS4 Credit Combinations y = -3sin0.5xo3www.mathsrevision.com210 90o 180o270o360o -1 -2 -3created by Mr. Lafferty 36. Write downy = 1.5cos2xoequations for the graphs shown? Cosine y = -2cos2xoCombinationsS4 Credit y = 0.5cos4xo 3www.mathsrevision.com 2 1 090o 180o270o360o-1 -2 -3 created by Mr. Lafferty 37. Combination GraphsS4 Creditwww.mathsrevision.com Now Try MIA Ch11 Ex 5.1Page 227 created by Mr. Lafferty 38. C moves the graph Trigonometry Graphs = 360 up or down in thePeriodoy-axis directionbS4 Credit y = a sin (bx) + cwww.mathsrevision.comHow many times it repeatsa - Amplitude itself in 360oFor a > 1 stretches graph in the y-axis directionFor a < 1 compresses graph in the y - axis direction For a - negative flips graph in the x axis.created by Mr. Lafferty 39. Sine GraphS4 CreditSimply movegraph up by 1www.mathsrevision.com 1 045o90o 180o270o 360o Given the basic y = sin x-1 graph what does thegraph of y = sin x + 1 looklike? created by Mr. Lafferty 40. Cosine GraphGiven the y = cos x graph.What does the graph ofy = cos x 0.5 look like?S4 Credit Simply move down by 0.5www.mathsrevision.com 1 090o 160 180o o270o 360o-1 created by Mr. Lafferty 41. Write downequations for graphs shown ? Trig Graph= 0.5sin2x y o + 0.5Combinationsy = 2sin4x - 1oS4 Credit 3www.mathsrevision.com 21090o 180o270o 360o -1-2-3created by Mr. Lafferty 42. Write downequations for the graphs shown? Cosiney = cos2xo + 1Combinationsy = -2cos2x - 1oS4 Credit 3www.mathsrevision.com 2 1 090o 180o270o 360o-1 -2 -3 created by Mr. Lafferty 43. Combination GraphsS4 Creditwww.mathsrevision.com Now try MIACh11 Ex 5.2Page 231 created by Mr. Lafferty 44. StarterS4 Credit1. Make b the subject of the formulawww.mathsrevision.com c=b+d2. Use the quadratic formula to solve x + 6x + 223. Sketch the function y = 2sin4xcreated by Mr. Lafferty 45. Solving Trig EquationsS4 CreditLearning Intention Success Criteriawww.mathsrevision.com1. To explain how to solve 1. Use the rule for solving any trig equations of the form normal equation a sin xo + 1 = 0 2. Realise that there are manysolutions to trig equationsdepending on domain. created by Mr. Lafferty 46. Solving Trig EquationsS4 Creditwww.mathsrevision.com Sin +ve All +ve 180o - xo 180o + xo 360o - xo Tan +ve Cos +ve 1 2 34 created by Mr. Lafferty 47. Solving Trig Equations whatGraphicallyS4 Credita sin xo + b = 0 we trying to aresolveExample 1 :www.mathsrevision.comSolving the equation sin xo = 0.5 in the range 0o to 360osin xo = (0.5)xo = sin-1(0.5)xo = 30o There is another solution xo = 150o 12 3 4 created by Mr. Lafferty(180o 30o = 150o) 48. Solving Trig Equations whatGraphicallyS4 Credita sin xo + b = 0 we trying to aresolveExample 1 :www.mathsrevision.comSolving the equation 3sin xo + 1= 0 in the range 0o to 360o sin xo = -1/3 Calculate first Quad value xo = 19.5ox = 180o + 19.5o = 199.5o There is another solution12 34 ( 360o - 19.5o = 340.5o) created by Mr. Lafferty 49. Solving Trig Equations what GraphicallyS4 Credit a cos xo + b are we trying to=0 solveExample 1 :www.mathsrevision.comSolving the equation cos xo = 0.625 in the range 0o to 360ocos xo = 0.625xo = cos -1 0.625xo = 51.3o There is another solution (360o - 53.1o = 308.7o) 1 2 3 4 created by Mr. Lafferty 50. Solving Trig Equations whatGraphicallyS4 Credita tan xo + b are we trying to =0solveExample 1 :www.mathsrevision.comSolving the equation tan xo = 2 in the range 0o to 360otan xo = 2 xo = tan -1(2) xo = 63.4o There is another solution x = 180o + 63.4o = 243.4o123 4 created by Mr. Lafferty 51. Solving Trig EquationsS4 Creditwww.mathsrevision.comNow try MIA Ch11 Ex6.1, 6.2 and 7.1(page 236)created by Mr. Lafferty 52. StarterS4 Credit1. Make a the subject of the formulawww.mathsrevision.com 5 = 10b + a2. Use the quadratic formula to solve x + 5x + 123. Sketch the function y = 4sin3x created by Mr. Lafferty 53. Solving Trig EquationsS4 CreditLearning IntentionSuccess Criteriawww.mathsrevision.com1. To explain some special1. Know and learn the two trig relationshipsspecial trig relationships. sin 2 xo + cos 2 xo = ?2. Apply them to solveandproblems.tan xo and sin x cos xcreated by Mr. Lafferty 54. Solving Trig EquationsS4 CreditLets investigatewww.mathsrevision.comsin 2xo + cos 2 xo = ?Calculate value for x = 10, 20, 50, 250 sin 2xo + cos 2 xo = 1 Learn !created by Mr. Lafferty 55. Solving Trig EquationsS4 CreditLets investigatewww.mathsrevision.com sin xotan xoand cos xoCalculate value for x = 10, 20, 50, 250 sin xotan xo = cos xo Learn !created by Mr. Lafferty 56. Solving Trig EquationsS4 Creditwww.mathsrevision.comNow try MIA Ex8.1Ch11 (page 238)created by Mr. Lafferty