(a) Experiment with a calculator to find an interval 0 ::5 8 < 81, where 8 is measured

Chapter 3, Problem 22

(choose chapter or problem)

(a) Experiment with a calculator to find an interval 0 ::5 8 < 81, where 8 is measured in radians, for which you think sin 8 = 8 is a fairly good estimate. Then use a graphing utility to plot the graphs of y = x and y = sin x on the same coordinate axes for 0 ::5 x ::5 7T/2. Do the graphs confirm your observations with the calculator? {b) Use a numerical solver to plot the solutions curves of the initial-value problems and d28 -2 + sin 8 = 0, 8(0) = 80, 8'(0) = 0 dt d 2 8 -2 + 8 = 0, 8(0) = 80, 8' (0) = 0 dt for several values of 80 in the interval 0 ::5 8 < 81 found in part (a). Then plot solution curves of the initialvalue problems for several values of 80 for which 80>81.