Amare wants to ride a ferris wheel that sits four meters above the ground and has a diameter of 50 meters. it takes six minutes to do three revolutions on the ferris wheel. complete the function, h(t), which models amare's height above the ground, in meters, as a function of time, t, in minutes. assume he enters the ride at the low point when t = 0. h(t) = · sin( t + ) +

So, we know that she is at a height of 4 meters at t=0. She completes one revolution in 2 minutes, hence we need to take a term of sin(pi*t) for our function to have a period of 2 (remember, if a is the coefficient of t, the period of our function is 2*pi/a). Hence, we have that the function is of the form h(t)=b*sin(pi*t+a)+4. Since 4 is the lowest point, we need that the sin function takes its lowest value at t=0; it takes its lowest values at 3/2*pi, hence we get that a=3/2*pi. Also, the largest value that sinx gets is 1; hence, if b*sinx=50 is to hold, we have that b=50meters. Thus, the whole function is