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- 1. Drawing Trigonometric Graphs.
- 2. The Basic Graphs.You should already be familiar with the following graphs:Y = SIN X
- 3. Y= COS X
- 4. Y = TAN X
- 5. Changing Trigonometric Graphs.You should know how the following graphs differ from the basictrigonometric graphs:Y= 2 SIN X The 2 in front of the sin x changes the “amplitude” of the graph.
- 6. Y = 5 COS XAs expected the amplitude of the graph is now 5. Hence thegraph has a maximum value of 5 and a minimum value of –5.
- 7. Y = SIN 2X By introducing the 2 in front of the X , the “period” of the graph now becomes 360o ÷ 2 = 180o.
- 8. Y= COS 6XThe period of the graph has now become 360o ÷ 6 = 60o asexpected.
- 9. Y= SIN X + 1The plus 1 has the effect of “translating” the graph onesquare parallel to the y axis.
- 10. Y = COS X - 5 The cosine graph is translated 5 squares downwards parallel to the y axis.
- 11. Y= – SIN XThe minus sign in front of the function “reflects” the whole graphin the X axis.
- 12. Y = – COS X As expected the cosine graph is reflected in the X axis.
- 13. Summary Of Effects.(1) Y= K COS X & Y = K SINX +k -k The amplitude of the function is “K” .(2) Y = COS KX & Y = SIN KX 360 ÷ K The period of the function is “360 ÷ k” .
- 14. (3) Y= COS X + K & Y = SIN X + K +k -k Translates the graph + K or – K parallel to the y axis. (4) Y = - COS X & Y = - SIN X. Y = - COS X Reflects the graph in the x axis.
- 15. Combining The Effects.We are now going to draw more complex trigonometric graphslike the one shown above, by considering what each part of theequation does to the graph of the equation.
- 16. y = 4 sin xExample 1.Draw the graph of : 4 y = 4sin2x + 3Solution. y = 4 sin 2xDraw the graph of :y = sin x 180o y = 4sin 2x + 3 +3
- 17. Example 2 y = - 6cos5xDraw the graph y = 2 – 6 cos 5xSolution.Draw the graph of :y = cos x y = 2 – 6 cos 5xy= 6cos5x 72o 6
- 18. Creating A Phase Shift.Shown below is the graph of y = sin xoNow compare it with the graph of y= sin( x - 60o) + 60o The graph is translated 60o to the right parallel to the x axis.
- 19. Shown below is the graph of y = cos x.Now compare it to the graph of y = cos ( x + 45o) -45o The graph is translated 45o to the left parallel to the x axis.

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