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
[tex]h(t)=50*sin(\pi t+ \frac{3 \pi}{2} ) +4[/tex]
