Graphs of Sine and Cosine (VCE SSCE Mathematical Methods): Flashcards

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Graphs of Sine and Cosine
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Type of function: sine & cosine

Periodic functions

Period of y=sinxy = \sin x

2π2\pi

Amplitude of y=sinxy = \sin x

11

Period formula for y=asin(nt)y = a\sin(nt) or y=acos(nt)y = a\cos(nt)

2πn\frac{2\pi}{n}

Amplitude of y=asin(nt)y = a\sin(nt) or y=acos(nt)y = a\cos(nt)

aa

Range of y=asin(nt)y = a\sin(nt)

[a,a][-a, a]

y=cosxy = \cos x vs y=sinxy = \sin x (shift)

sinx\sin x shifted π2\frac{\pi}{2} units left

Effect of negative coefficient in y=asin(nt)y = -a\sin(nt)

Reflection in x-axis

Type of function: sine (odd/even)

Odd: sin(x)=sinx\sin(-x) = -\sin x

Type of function: cosine (odd/even)

Even: cos(x)=cosx\cos(-x) = \cos x

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