How do you find the amplitude, period, and shift for $y = 4 cos (\frac{x}{2} + \frac{π}{2})$ $y= 4cos(x/2+pi/2)$ ?

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How do you find the amplitude, period, and shift for $y = 4 cos (\frac{x}{2} + \frac{π}{2})$ $y= 4cos(x/2+pi/2)$ ?

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Answer 1 · 2015-11-21T12:00:40

The amplitude is 4, the period is $2 π$ $2pi$ , and there is an horizontal shift of $- \frac{π}{2}$ $-pi/2$

Explanation:

There is a general equation for cosine
$y = a \cdot cos (b (x - c)) + d$ $y = a*cos(b(x-c)) + d$
where $| a |$ $|a|$ is the amplitude
$2 \frac{π}{| b |}$ $2pi/|b|$ is the period
c is the horizontal displacement
and d is the vertical displacement

$| b |$ $|b|$ and $| a |$ $|a|$ mean the value of a or b without the sign ( that is no positive or negative attached to the value)

So for your equation of $y = 4 \cdot cos ((\frac{x}{2}) + (\frac{π}{2}))$ $y = 4*cos((x/2) + (pi/2))$
a = 4
b = 1
$c = - \frac{π}{2}$ $c = -pi/2$
d = 0
This makes your amplitude, 4
period, $2 π$ $2pi$
horizontal displacement $- \frac{π}{2}$ $-pi/2$
and no vertical displacement

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How do you find the amplitude, period, and shift for $y = 4 cos (\frac{x}{2} + \frac{π}{2})$ $y= 4cos(x/2+pi/2)$ ?

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Explanation:

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How do you find the amplitude, period, and shift for $y = 4 cos (\frac{x}{2} + \frac{π}{2})$ $y= 4cos(x/2+pi/2)$ ?