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Published byElijah Clarke Modified over 2 years ago

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

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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 –

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y = sin x x –2 –3 /2– – /2 0 /2 3 /22 5 /23 7 /24 sin x010– y = cos x x –2 –3 /2– – /2 0 /2 3 /22 5 /23 7 /24 cos x10– –2 0 1 –1 3 – /23 /25 /27 /2– /2–3 /2 2 4 – 0 3 – /23 /25 /27 /2– /2–3 /2 y = sin x and y = cos x are called periodic functions because of the repeating cycles. For sine, its For cosine, its: 1 –1

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y = sin x x0 /2 3 /22 sin x010–10 y = –sin x Reflect y = sin x over the x-axis x0 /2 3 /22 –sin x0–1010 y = cos x x0 /2 3 /22 cos x10–101 y = –cos x Reflect y = cos x over the x-axis x0 /2 3 /22 –cos x– /23 / –1 /23 / –1 /23 / –1 /23 /2

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Sketching y = a sin x x0 /2 3 /22 sin x010–10 2 sin x020–20 y = 2 sin x x0 /2 3 /22 sin x010–10 ½ sin x01/20–1/20 y = ½ sin x x 0 /2 3 /22 sin x 010–10 –3sinx 0–3030 y = –3 sin x Sketching y = a cos x x0 /2 3 /22 cos x10–101 –2 cos x–2020 y = –2 cos x x0 /2 3 /22 cos x10–101 ¾ cos x¾0–¾0¾ y = ¾ cos x x0 /2 3 /22 cos x10–101 –4 cos x–4040 y = –4 cos x –1 /23 /2 2 –2 y = 2 sin x y = sin x y = ½ sin x 3 –3 2 0 /23 / –2 /23 /2 y = –2 cos x 2 0 ¾ –¾ /23 / –4 /23 /2 y = –4 cos x 2 0 ½ –½ /23 /2 1 –1 y = –cos x –1 1 y = ¾ cos x

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To be replaced by Ryder 1

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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 = 2 /|b| 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: 2 Frequency: 3Period: 2 /3 g(x) = –2 sin (¾x)Amplitude: 2 Frequency: 3/4Period: 2 /(¾) = 8 /3 How many times do they intersect on the interval [0, 2 ]? 6 times Give a solution for the equation 2 cos (3x) = –2 sin (¾x) on [0, 2 ]: –1 –2 –3 f(x) = 2 cos (3x) g(x) = –2 sin (¾x)

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