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The following points are a minimum and a maximum of a sinusoid. Complete the following steps to
model the curve using the sine function.

(4.5, 2), (1.5, 22)

a) What is the vertical shift, k, of this curve?

b) What is the amplitude, a, of this curve?

c) What is period and frequency factor, b, of this curve?

d) Write an equation using the sine function that models this curve.

Respuesta :

Answer: K= 12

A=10

P= 6

B=pi/3

Equation: y=10sin(pi/3(x))+12

Step-by-step explanation: You can find k by finding the midline, or adding the minimum and maximum y values together and then dividing by 2.

You find a by using the midline value (12) and subtracting it from the maximum y value to get the amplitude.

To find the period, find the difference between the min and max x values, which is 3, then double it to get the full period.

To find the b value, plug it into the 2pi/b=p equation, using the period value you found before you should get pi/3.

When assembling the equation use this format: y=asin[b(x-h)]+k.

You can also graph it with a graphing calculator to check to be sure the max and min points line up.

MrRoyal

A sine function is represented as: [tex]\mathbf{y = A\sin(Bx) + k}[/tex]

  • The vertical shift is 12
  • The amplitude is 10
  • The period is 6, and the frequency factor is [tex]\mathbf{\frac{\pi}{3}}[/tex].
  • The sine function is [tex]\mathbf{y = 10\sin(\frac{\pi}{3}x) + 12}[/tex]

The given parameters are:

[tex]\mathbf{(x_1,y_1) = (4.5,2)}[/tex]

[tex]\mathbf{(x_2,y_2) = (1.5,22)}[/tex]

(a) The vertical shift (k)

The vertical shift is calculated using:

[tex]\mathbf{k = \frac{y_1 + y_2}{2}}[/tex]

So, we have:

[tex]\mathbf{k = \frac{2 + 22}{2}}[/tex]

[tex]\mathbf{k = \frac{24}{2}}[/tex]

[tex]\mathbf{k = 12}[/tex]

(b) The amplitude (A)

The amplitude is calculated using:

[tex]\mathbf{A = \frac{y_2 - y_1}{2}}[/tex]

So, we have:

[tex]\mathbf{A = \frac{22 - 2}{2}}[/tex]

[tex]\mathbf{A = \frac{20}{2}}[/tex]

[tex]\mathbf{A = 10}[/tex]

(c) The period (p) and the frequency factor (b)

The period is calculated using:

[tex]\mathbf{p = x_1 + x_2}[/tex]

So, we have:

[tex]\mathbf{p = 4.5 + 1.5}[/tex]

[tex]\mathbf{p = 6}[/tex]

The frequency factor (b) is calculated using:

[tex]\mathbf{b = \frac{2\pi}{p}}[/tex]

So, we have:

[tex]\mathbf{b = \frac{2\pi}{6}}[/tex]

[tex]\mathbf{b = \frac{\pi}{3}}[/tex]

(d) The equation of the sine function

A sine function is represented as:

[tex]\mathbf{y = A\sin(Bx) + k}[/tex]

So, we have:

[tex]\mathbf{y = 10\sin(\frac{\pi}{3}x) + 12}[/tex]

Read more about sine functions at:

https://brainly.com/question/1368748

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