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

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Effect of Changing 'n' in aSin(nx) or aCos(nx)
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Amplitude in sine/cosine functions

Max or min value of function

Default amplitude of sin⁡x\sin x, cos⁡x\cos x

11

Period in sine/cosine functions

Length of one complete cycle

Default period of sin⁡x\sin x, cos⁡x\cos x

2π2\pi

Starting point of y=sin⁡xy = \sin x graph

(0,0)(0, 0)

Starting point of y=cos⁡xy = \cos x graph

(0,1)(0, 1)

Symmetry type: sin⁡x\sin x

Odd function

Symmetry type: cos⁡x\cos x

Even function

Peak value of sin⁡x\sin x and cos⁡x\cos x

11

Trough value of sin⁡x\sin x and cos⁡x\cos x

−1-1

Period formula for asin⁡(nx)a\sin(nx) or acos⁡(nx)a\cos(nx)

T=2π∣n∣T = \frac{2\pi}{|n|}

Applications of sine/cosine graphs

Waves, vibrations, periodic behaviours

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