# Math Grade 11, Sinusoidal functions Please state the period, amplitude, max/min values, range, domain, horizontal phase shift, and vertical displacement, of each of the above functions. please answer clearly and distinct the answer for each one, clearly. thanks.

The general form of a sinusoid is:

`y=Asin(B(x-h))+k`

A: A is the amplitude. If A<0 the base function is reflected over the horizontal axis. (A is a vertical stretch/compression.)

B: B affects the period (it is a horizontal stretch/compression.) The period is `p=(2pi)/B` . If B<0 the base function is reflected over the y-axis.

h: h is a horizontal translation (phase shift.)

k: k is a vertical translation. It provides the midline for the sinusoid.

Given `y=-3cos(2x-30^@)+1`

Rewrite as `y=-3cos(2(x-15^@))+1`

The base function is the cosine function.

(1)The midline (vertical displacement is up 1) is y=1.

(2) The amplitude is 3

(3) The maximum value is 4 (3 units above the midline) while the minimum value is -2.

(4) The domain is all real numbers; the range is `-2<=y<-4`

(5) The horizontal phase shift is 15 units right. (`pi/12` units right)

(6) The function is reflected across the line y=1.

(7) The period is `p=(2pi)/2=pi` units.

The graph:

(Horizontal axis is in radians instead of degrees.)

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