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CHAPTER 1:  TRIGONOMETRY 2 Why study these trigonometric graphs? Chapter 1 : Trigonometry 2
[object Object],[object Object],Chapter 1 : Trigonometry 2
1.1 Graphs of Trigonometric Functions 1.1.1 The Sine Curve Chapter 1 : Trigonometry 2 How does the sine curve look like? Let us consider the graph of the function  f ( x ) = sin x. Its easier to calculate the values in  Deg mode
Chapter 1 : Trigonometry 2 1.1.2 The Cosine Curve How does the cosine curve look like? Let us consider the graph of the function  f ( x ) = cos x.
3 important term used in sketching a trigonometric graph :  ,[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 1 : Trigonometry 2
3 important term used in sketching a trigonometric graph :  ,[object Object],[object Object],[object Object],[object Object],Chapter 1 : Trigonometry 2
Example 1 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 1 : Trigonometry 2 Determine the period, amplitude and phase shift of  y  = 5 sin 4 x . y  = 5 sin 4 x . a b
Example 2 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 1 : Trigonometry 2 Determine the period, amplitude and phase shift of  y = -2 cos (x – 3). y = -2 cos (x – 3) . a b c
Example 3 ,[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 1 : Trigonometry 2 Determine the period, amplitude and phase shift of  y = -4 sin 3(x + 2). y = -4 sin 3(x + 2) . a b c
[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 1 : Trigonometry 2 Determine the period of  y = cos 3x  and sketch the graph of one period beginning at x = 0 . Example 4 x 0° 30° 60° 90° 120° y = cos 3x 1 0 -1 0 1
[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 1 : Trigonometry 2 Determine the period and amplitude of  y = -3 sin 0.5x  and sketch the graph of one period beginning at x = 0 . Example 5 x 0° 180° 360° 540° 720° sin 0.5x 0 1 0 -1 0 -3 sin 0.5x 0 -3 0 3 0
[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 1 : Trigonometry 2 Determine the period, amplitude and the phase shift of  y = 3 sin (x-  π )   and sketch the graph for Example 6 x 0° 90° 180° 270° 360° (x- π ) (x-180 °) -180° -90° 0° 90° 180° 3sin  (x- π ) 0 -3 0 3 0
[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 1 : Trigonometry 2 Determine the period, amplitude and the phase shift of  y = 2 sin (x +  π /2)   and sketch the graph for Example 7 Try Ex 5 pg 9 x 0° 90° 180° 270° 360°
[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 1 : Trigonometry 2 Determine the period, amplitude and the phase shift of  y = 2.5 cos(3x – π )   and sketch the graph for Example 8 y = 2.5 cos 3(x –  π / 3) . Factorize b x
[object Object],[object Object],[object Object],[object Object],[object Object],Chapter 1 : Trigonometry 2 Determine the period, amplitude and the phase shift of  y = 2+3 sin (x-  π )   and sketch the graph for Example 9 Try  Tut 1 pg 203 - 205 x 0° 90° 180° 270° 360° (x- π ) -180° -90° 0° 90° 180° 3sin  (x- π ) 0 -3 0 3 0 2+3sin  (x- π ) 2 -1 2 5 2
Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Chap 1 trigonometry 2 part 1

  • 1. CHAPTER 1: TRIGONOMETRY 2 Why study these trigonometric graphs? Chapter 1 : Trigonometry 2
  • 2.
  • 3. 1.1 Graphs of Trigonometric Functions 1.1.1 The Sine Curve Chapter 1 : Trigonometry 2 How does the sine curve look like? Let us consider the graph of the function f ( x ) = sin x. Its easier to calculate the values in Deg mode
  • 4. Chapter 1 : Trigonometry 2 1.1.2 The Cosine Curve How does the cosine curve look like? Let us consider the graph of the function f ( x ) = cos x.
  • 5.
  • 6.
  • 7.
  • 8.
  • 9.
  • 10.
  • 11.
  • 12.
  • 13.
  • 14.
  • 15.
  • 16.