How do I determine the amplitude, period, and phase shift for this function? $y = - 2 cos (\frac{π}{2} x + π)$ $y=-2cos(pi/2x+pi)$

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Answer 1 · 2018-03-20T01:43:13

When given an equation of the form $y = A cos (B x + C) + D$ $y = Acos(Bx+C)+D$ :

$Amplitude = | A |$ $"Amplitude" = |A|$

$Period = \frac{2 π}{| B |}$ $"Period" = (2pi)/|B|$

$Phase shift = - \frac{C}{B}$ $"Phase shift" = -C/B$

$Vertical shift = D$ $"Vertical shift "= D$

Using above information on the given equation, $y = - 2 cos (\frac{π}{2} x + π)$ $y=-2cos(pi/2x+pi)$ :

$Amplitude = | - 2 |$ $"Amplitude" = |-2|$

$Amplitude = 2$ $"Amplitude" = 2$

$Period = \frac{2 π}{∣ ∣ \frac{π}{2} ∣ ∣}$ $"Period" = (2pi)/|pi/2|$

$Period = 4$ $"Period" = 4$

$Phase shift = - \frac{π}{\frac{π}{2}}$ $"Phase shift" = -pi/(pi/2)$

$Phase shift = - 2$ $"Phase shift" = -2$

How do I determine the amplitude, period, and phase shift for this function? y=−2cos(π2x+π)y=-2cos(pi/2x+pi)