Effect of Changing 'a' in aSin(nx) or aCos(nx) (Leaving Cert Mathematics): Flashcards

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Effect of Changing 'a' in aSin(nx) or aCos(nx)
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Parameter aa in asin⁡(nx)a\sin(nx) affects

Amplitude

Amplitude definition

Maximum vertical displacement from y=0y = 0

Amplitude formula

∣a∣|a|

Effect of ∣a∣>1|a| > 1

Vertical stretch, taller wave

Effect of 0<∣a∣<10 < |a| < 1

Vertical compression, shorter wave

Effect of a<0a < 0

Vertical flip across xx-axis

Role of aa in trig graphs

Vertical stretch or compression

Does aa affect period?

No, period determined by nn

Amplitude of y=2sin⁡(x)y = 2\sin(x)

22

Amplitude of y=0.5sin⁡(x)y = 0.5\sin(x)

0.50.5

Amplitude of y=−3cos⁡(x)y = -3\cos(x)

33

What determines period in asin⁡(nx)a\sin(nx)?

nn, not aa

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