Suppose That the Formula $A(t)=-\frac{1}{4} \cos \frac{\pi}{8} t+\frac{1}{4}$ Describes the Motion Formed by a Rhythmically Moving Arm During

Essay

Suppose that the formula $A(t)=-\frac{1}{4} \cos \frac{\pi}{8} t+\frac{1}{4}$ describes the motion formed by a rhythmically moving arm during a 16 minute time period where $A(t)$ is the angle (in radians) formed by the arm at time $t$ (in minutes).
(a) Give the domain and range of $A$ .
(b) Graph $A(t)$ over its domain.
(c) Use the graph to determine the maximum and minimum values of $A(t)$ and when they occur.
(d) Find $A(6)$ analytically and check your result graphically. Use symmetry to find $A(10)$ .
(e) When is the angle $\frac{1}{4}$ radians?
(f) Write the equation $A=-\frac{1}{4} \cos \frac{\pi}{8} t+\frac{1}{4}$ as an equation involving arcsine by solving for $t$ .