angl2aCab6ethm angl2aCab6ethm
  • 19-11-2016
  • Mathematics
contestada

What is the amplitude, period, and phase shift of y= 5cos( x/2 + 2pi/3)

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alsteva alsteva
  • 23-11-2016
y = A cos(Bx + C)
A - amplitude
[tex] \frac{2\pi}{B} [/tex] - period
[tex]- \frac{C}{B} [/tex] - phase shift

[tex]y=5\cos{( \frac{x}{2} + \frac{2\pi}{3} )} \\ \\y=5\cos{( \frac{1}{2}x + \frac{2\pi}{3})} \\ \\A=5,B= \frac{1}{2},C= \frac{2\pi}{3}[/tex]

Amplitude: 5
Period: [tex] \frac{2\pi}{B}=\frac{2\pi}{\frac{1}{2}}=4\pi [/tex]
Phase shift: [tex]- \frac{C}{B} =- \frac{\frac{2\pi}{3}}{\frac{1}{2}}= -\frac{4\pi}{3} [/tex]
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