Chap 1 trigonometry 2 part 1

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]

Chap 1 trigonometry 2 part 1

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