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## Feb 11, 2011

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**Feb 11, 2011**The transformed trigonometric functions**f(x) = a sin b(x – h) + k**• Recall which is which in the rule:**Match the parameters to the number:**k h b a 5 7 4 1**Which is affected by parameter a?**a = 1 Amplitude Period Frequency l.o.o.**Which is affected by parameter a?**a = 2 Amplitude Period Frequency l.o.o.**Which is affected by parameter a?**a = 3 Amplitude Period Frequency l.o.o.**Which is affected by parameter a?**Amplitude Period Frequency l.o.o.**In fact, parameter a = amplitude**Amplitude Period Frequency l.o.o.**y = 2 cos x**y = 8 sin 2x y = -3 cos x y = 4 sin 9x - 2 What would be the amplitude:**y = 2 cos x**y = 8 sin 2x y = -3 cos x y = 2.4 sin 9x - 2 amplitude = 2 amplitude = 8 amplitude = 3 amplitude = 2.4 What would be the amplitude:**Another way to find amplitude:**Amplitude = half the distance between the Max and min values = (M – m) 2 = (2 - -6) 2 = 8 2 = 4**Another way to find amplitude:**Amplitude = half the distance between the Max and min values = (M – m) 2 = (2 - -6) 2 = 8 2 = 4 2 -6**What would be the value of a in the rule?**a = 1 Amplitude = half the distance between the Max and min values = (M – m) 2 = (2 - 0) 2 = 2 2 = 1**In general then:**• For f(x) = a sin b(x – h) + k OR: • f(x) = a cos b(x – h) + k Amplitude =**In general then:**• For f(x) = a sin b(x – h) + k OR: • f(x) = a cos b(x – h) + k Amplitude = |a|**In general then:**• For f(x) = a sin b(x – h) + k OR: • f(x) = a cos b(x – h) + k Amplitude = |a|**Which is affected by parameter b?**b = 1 Amplitude Period Frequency l.o.o.**Which is affected by parameter b?**b = 2 Amplitude Period Frequency l.o.o.**Which is affected by parameter b?**b = 4 Amplitude Period Frequency l.o.o.**Which is affected by parameter b?**Amplitude Period Frequency l.o.o.**Which is affected by parameter b?**4 cycles Amplitude Period Frequency l.o.o.**Which is affected by parameter b?**Amplitude Period Frequency l.o.o.**In fact, b = frequency**y = sin 4x Amplitude Period Frequency = 4 = b l.o.o.**y = cos 4x**y = 8 sin 2x y = -3 cos (x + 1) -2 y = 2.4 sin (-9x) - 2 What would be the frequency:**y = cos 4x**y = 8 sin 2x y = -3 cos (x + 1) -2 y = 2.4 sin (-9x) - 2 frequency = 4 frequency = 2 frequency = frequency = 9 What would be the frequency:**In general then:**• For f(x) = a sin b(x – h) + k OR: • f(x) = a cos b(x – h) + k Frequency =**In general then:**• For f(x) = a sin b(x – h) + k OR: • f(x) = a cos b(x – h) + k Frequency = |b|**And if 4 cycles have a total width of 2.... ...then one**of those cycles must have a width of... y = sin 4x Amplitude Period Frequency l.o.o.**And if 4 cycles have a total width of 2.... ...then one**of those cycles must have a width of... y = sin 4x Amplitude Period Frequency l.o.o. ?**And if 4 cycles have a total width of 2.... ...then one**of those cycles must have a width of... y = sin 4x Amplitude Period = Frequency l.o.o.**And if 4 cycles have a total width of 2.... ...then one**of those cycles must have a width of... y = sin 4x Amplitude Period = Frequency l.o.o.**In fact, period =**y = sin 4x Amplitude Period = Frequency l.o.o.**In fact, period =**y = sin 4x Amplitude Period = Frequency l.o.o.**y = cos 4x**y = 8 sin 2x y = -3 cos (x + 1) -2 y = 2.4 sin (-9x) - 2 period = period = period = period = What would be the period:**y = cos 4x**y = 8 sin 2x y = -3 cos (x + 1) -2 y = 2.4 sin (-9x) - 2 period = period = period = period = What would be the period:**In general then:**• For f(x) = a sin b(x – h) + k OR: • f(x) = a cos b(x – h) + k Frequency = |b| Period =**Which is affected by parameter h?**h = 0 Amplitude Period Frequency l.o.o.