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 $t$.

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The Answer of 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 $t$.

Suppose That the Formula A(t)=13sin⁡π4t+23A(t)=\frac{1}{3} \sin \frac{\pi}{4} t+\frac{2}{3}A(t)=31​sin4π​t+32​ Describes the Motion Formed by a Rhythmically Moving Arm During

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