Question

The following sinusoid is plotted below. Complete the following steps to model the curve using the cosine function.

Answer 1

Answer:

A.) phase shift is h=6

B.) Vertical shift is 21 units down

C.) The amplitude is 5 from the midline at y= -21

D.) The period is 16 and the frequency factor is pi/8

E.) 5 cos(pi/8(x-6))-21

Step-by-step explanation:

Find your minimum and maximum values. This would help you find the amplitude and the vertical shift. To find amplitude, the formula is A= (absolute value) of the max minus the min and divide by 2. To find vertical shift, you add the max and min values and divide by 2. The period is the distance of the max and min values and then doubled. The distance was 8 units so the period was 16. To find frequency factor, just plug in your values. You know that the formula is Period= 2pi/b. So it would be 16= 2pi/b. The frequency factor should be pi/8 after you cross multiply and then divide. To write the equation, you substitute the values into the equation of acos(b(x-c))+d. Make sure to put parentheses or else the graph will look wrong.