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# Trigonometric graphs

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Trig Graphs

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### Trigonometric graphs

1. 1. Block 3 Trigonometric Graphs
2. 2. What is to be learned? • A reminder of how to draw and identify trig graphs. • Take it a bit further.
3. 3. 90 180 270 360 1 0 -1 Y = sinx Maximum Value = 1 Minimum Value = -1
4. 4. 90 180 270 360 1 0 -1 Y = cosx Maximum Value = 1 Minimum Value = -1
5. 5. 90 180 270 360 7 0 -7 Y = 7sinx Maximum Value = 7 Minimum Value = -7 Range = Max - Min Range = 7 – (-7) = 14 →range = 14 Range
6. 6. 90 180 270 360 4 0 -4 Y = 4cosx Maximum Value = 4 Minimum Value = -4 →range = 8
7. 7. 90 180 270 360 8 0 -8 Y = - 8sinx Maximum Value = 8 Minimum Value = -8 “Opposite” to Sin x
8. 8. 90 180 270 360 6 0 -6 Y = - 6cosx Maximum Value = 6 Minimum Value = -6 “Opposite” to Cos x
9. 9. 900 1800 2700 3600 900 1800 2700 3600 3 -3 6 -6 Write the Equations 1. 2. y = -3sinx y = -6cosx y = 9sinx y = cosx 3. 4. 9 -9 1 -1 900 1800 2700 3600 900 1800 2700 3600
10. 10. 90 180 270 360 1 0 -1 Y = sin x 540450 Period of graph is 3600 Cycle starts again Also applies to Y = cos x Between 00 and 3600 there is 1 cycle Taking it Further
11. 11. 90 180 270 360 1 0 -1 Y = sin 2x Period of graph is 1800 There are 2 cycles between 00 and 3600
12. 12. Combining these rules Draw y = 6sin2x Max 6 Min -6 2 cycles Period = 360 ÷ 2 = 1800 90 180 270 360 6 0 -6 Y = 6sin 2x
13. 13. Recognising Graph Max 8 Min -8 4 cycles 90 180 270 360 8 0 -8 Y = 8cos4x Cosine
14. 14. 900 1800 2700 3600 900 1800 2700 3600 900 1800 2700 3600 900 1800 2700 3600 7 -7 5 -5 3 - 3 2 -2 Write the Equations 1. 2. 3. 4. y = 7sin2x y = 5cos2x y = 3cos4x y = 2sin3x
15. 15. Changing the Scale Nice for Drawing Graphs  y = 4 Sin 6x Cycles? Period 6 360 ÷ 6 = 600 15 30 45 60 4 0 -4
16. 16. 300 600 900 1200 7 Not so nice for recognising graphs  Period = 1200 No of Cycles in 360? 360 ÷ 120 = 3 y = 7 cos 3x 2400 3600
17. 17. Find equation of graph below. Cycles Max 7 Negative sin 360 ÷ 60 = 6 15 30 45 60 7 0 -7 y = -7sin6x
18. 18. Remember rules for y = (x – 3 )2 + 5 Same rules for trig graphs! 3 units to right Up 5 Extra Trig Graph Rules
19. 19. 90 180 270 360 4 0 -4 Y = 4cos (x – 450 ) 450 Y = 4cosx 450 to right Sketch Normal Graph Move each point right/left y =4cos(x – 450 )
20. 20. 90 180 270 360 11 0 -11 Recognising Sin Graph 300 to right y = 11 sin(x – 300 ) 300
21. 21. 90 180 270 360 13 0 -13 Recognising Cos Graph 200 to left y = 13 cos(x + 200 ) -200
22. 22. 90 180 270 360 11 0 -11 A Bit of Confusion Sin Graph 300 to left y = 11 sin(x + 300 ) -300 600 Cos Graph 600 to right y = 11 cos(x – 600 ) Both correct
23. 23. 6 -6 y = 6cos(x + 300 ) -300 Identify this graph 900 1800 2700 3600
24. 24. 90 180 270 360 1 0 -1 Y = sinx + 2 Y = sinx 2 3
25. 25. 90 180 270 360 4 0 -4 Y = 4cosx + 6 8 12 range = 8 Graph Type y = 4cosx 2 6 10 -2 Equation?
26. 26. 90 180 270 360 0 No Maximum (or minimum) What about y = Tanx ??? Goes to infinity Cycle complete Period is 1800
27. 27. 90 180 270 360 0 Changing the period Cycle complete Normal Period is 1800 2 cycles y = tan2x
28. 28. 90 180 270 360 0 y = -Tanx
29. 29. Also Can now use radians!
30. 30. 90 180 270 360 1 0 -1 Y = sinx π /2 π 3π /2 2π
31. 31. Trigonometric Graphs Follow all the same rules as other function graphs. Range is handy for identifying (max – min) e.g. for y = 7sinx →range = 14
32. 32. π /2 π 2π 2 0 -2 y = 2cos(x – π /4) 4 6 y = 2cosx Sketch y = 2cos(x – π /4) + 1 y = 2cos(x – π /4) + 1 3π /2
33. 33. 0 -2 -4 Sketch y = 3sin(x + π /4) – 1 Y = 3sinx 2 4 Y = 3sin(x + π /4) Y = 3sin(x + π /4) – 1 Key Question 2π 3π /2ππ /2