Trigonometry Question

Question

A sewing machine has a wheel that turns as the machine sews. The wheel is 8 feet in diameter. The highest point of the handle at the edge of the wheel is 10 feet above the ground, and the lowest point is 2 feet above the ground. The wheel makes a complete turn every 4 seconds. Which of the following is a good model for the height (H, in feet) of the handle as a function of time (t, in seconds), given that the handle is its highest possible point at t=0 ?

A. H(t)=4cos((π*t)/2)+6

B. H(t)=4sin((π*t)/2)+6

C. H(t)=4cos((π(t-3))/2)+6

D. H(t)=4sin((π(t-3))/2)+6

E. H(t)= –4cos((π*t)/2)+6

Answer 1

As handle is at the highest point at t= 0

H(0) = 10 ft from ground

For Ans A

H(0) = 4 Cos(0) +6 = 4*1 +6 = 10

Which is the correct Answer

Answer 2

to be at its highest point when t=0, the sine or cosine of the angle has to = 1

D is correct

sin(pi(t-3)/2) = sin(pi(0-3)/2)= sin(-3pi/2) = sin(pi/2) =

sin(90 degrees) = 1

general equation is H(t) = Asin(Bt + C) + D

A=4 = amplitude

2pi/B = period = 4 seconds

B=2pi/4 = pi/2

C = phase shift = -3pi/2

D= vertical shift = 6

H(t) = 4sin(pi(t)/2 -3pi/2) + 6 = 4sin(pi(t-3)/2) +6