Question

Suppose that an airplane is asked to stay within a holding pattern near the airport. The function d(t) = 70sin(0.65t) + 150 represents the distance d (miles), the airplane is from the airport at time t (minutes). During the first 10 minutes after the plane enters the holding pattern at t = 0, at what time(s) t (if any) is the plane exactly 100 miles from the airport?

Answer 1

solve the equation
70sin(0.65t)+150= 100
where the angle (0.65t) is understood to be in radians
simplifying we get
sin(theta)= -5/7 where theta= 0.65*t

There are 2 solutions for theta in the range between 0 and 2pi
theta1= -0.796+2*pi= 5.488
theta2= pi- (-0.796)= 3.937

so t= theta1/0.65= 8.443 seconds
and t= theta2/0.65= 6.057 seconds