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Sketching y = a sin bx and y = a cos bx. x 0 30 45 60 90 120 135 150 180 210 225 240 270 300 315 330 360 sin x0.5.71.871.71.50–.5–.71–.87–1–.87–.71–.50.

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Presentation on theme: "Sketching y = a sin bx and y = a cos bx. x 0 30 45 60 90 120 135 150 180 210 225 240 270 300 315 330 360 sin x0.5.71.871.71.50–.5–.71–.87–1–.87–.71–.50."— Presentation transcript:

1 Sketching y = a sin bx and y = a cos bx

2 x sin x –.5–.71–.87–1–.87–.71– –1 0.5 – x cos x –.5–.71–.87–1–.87–.71– y = sin x y = cos x –1 0.5 –

3 y = sin x x –2 –3 /2– – /2 0 /2 3 /22 5 /23 7 /24 sin x y = cos x x –2 –3 /2– – /2 0 /2 3 /22 5 /23 7 /24 cos x

4 y = sin x x0 /2 3 /22 sin x y = –sin x x0 /2 3 /22 –sin x y = cos x x0 /2 3 /22 cos x y = –cos x x0 /2 3 /22 –cos x

5 Sketching y = a sin x x0 /2 3 /22 sin x 2 sin x y = 2 sin x x0 /2 3 /22 sin x 2 sin x y = ½ sin x x 0 /2 3 /22 sin x 2 sin x y = –3 sin x Sketching y = a cos x x0 /2 3 /22 cos x –2 cos x y = –2 cos x x0 /2 3 /22 cos x ¾ cos x y = ¾ cos x x0 /2 3 /22 cos x –4 cos x y = –4 cos x

6 To be replaced by Ryder 1

7 Sketching y = a sin bx and y = a cos bx: |a| = amplitude = ½(y max – y min ) i.e., the height from the middle to the top |b| = frequency = number of cycles in 2 units P = period = the least number of positive units it takes to complete one cycle Plot the two functions f(x) and g(x) on the same graph on 0 x 2. For each function, identify the amplitude, frequency, period and answer the number of times they intersect. f(x) = 2 cos (3x) Amplitude: ____ Frequency: ____Period: ____ g(x) = –2 sin (¾x)Amplitude: ____ Frequency: ____Period: ____ How many times do they intersect on the interval [0, 2 ]? ___ –1 –2 –3


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