# How do you find the amplitude, period, and shift for #y = -5sin(x/2)#?

Amplitude

Period

Shift

The Vertical Shift (D) = 0

Investigate the graph given below:

The General Form of the equation of the Cos function:

A represents the Vertical Stretch Factor and its absolute value is the Amplitude.

B is used to find the Period (P):

C, if given, indicates that we have a place shift BUT it is NOT equal to

The Place Shift is actually equal to

D represents Vertical Shift.

We observe that

Amplitude

Period

Shift

The Vertical Shift (D) = 0

Hope this helps.

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To find the amplitude, period, and shift for the function ( y = -5\sin\left(\frac{x}{2}\right) ):

Amplitude: The amplitude of a sine function is the absolute value of the coefficient of the sine function. In this case, the amplitude is ( | -5 | = 5 ).

Period: The period of a sine function is determined by the coefficient of ( x ) inside the sine function. The period ( T ) is calculated as ( T = \frac{2\pi}{b} ), where ( b ) is the coefficient of ( x ). So, for ( y = -5\sin\left(\frac{x}{2}\right) ), the period ( T ) is ( \frac{2\pi}{\frac{1}{2}} = 4\pi ).

Shift: The shift of a sine function is any horizontal translation to the left or right. In the form ( y = A\sin(b(x - h)) + k ), ( h ) represents the horizontal shift. For ( y = -5\sin\left(\frac{x}{2}\right) ), there is no horizontal shift, so ( h = 0 ).

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