Suppose That the Formula $A(t)=\frac{1}{3} \sin \frac{\pi}{4} t+\frac{2}{3}$ Describes the Motion Formed by a Rhythmically Moving Arm During

Essay

Suppose that the formula $A(t)=\frac{1}{3} \sin \frac{\pi}{4} t+\frac{2}{3}$ describes the motion formed by a rhythmically moving arm during an 8-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 $A(1)$ analytically and check your result graphically. Use symmetry to find $A(3)$ .
(e) When is the angle $\frac{2}{3}$ radians?
(f) Write the equation $A=\frac{1}{3} \sin \frac{\pi}{4} t+\frac{2}{3}$ as an equation involving arcsine by solving for $t$ .