Write the equation of the sinusoid as a sine curve Write the

Write the equation of the sinusoid as a sine curve. Write the equation of the sinusoid as a cosine curve. Write the equation of the sinusoid as a cosine curve. Write the equation of the sinusoid as a sine curve. Write the equation of the sinusoid as a sine curve. Write the equation of the sinusoid as a cosine curve.

Solution

9)

Sine normally starts at the midline at x = 0
Here midline = (12- 4)/2 = 4

Notice that when y = 4, x = pi/4

So, this is a shift rightward by pi/4

Now, amplitud = (max-min)/2
A = (12 - (-4))/2
A = 8

Midline or vertical shift, D = (max + min)/2 = (12 + -4)/2 = 4

Phase, shift C = pi/4 rightward, so positive pi/4

And Period from the curve :
First max happens when x = -5pi/4
Second max hapens when x = 3pi/4
Difference = period = 2pi
So, constant B = 2pi/period
B = 2pi/2pi
B = 1

So, using all this
y = Asin[B(x - C)] + D
becomes

y = 8sin(x - pi/4) + 4 ----> ANSWER

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10)
Usual cos starts at max when x = 0

Here, max occurs when x = 180 degrees, so rightshift by 180

So, C = 180 degrees

Period = 1620 - 180 = 1440

Constant B = 360/period
B = 360/1440 = 0.25

MAx = 5 and min = -11

So, amplitude A = (max - min)/2 = A = 8

Vertical shuft, D = (max + min)/2 = -3

So, we have :
y = Acos[B(x - C)] + D becomes

y = 8cos[0.25(x - 180)] - 3 ----> ANSWER

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