Answer
$t = \frac{3}{4\pi}~arcsin(3y)$
Work Step by Step
$y = \frac{1}{3}sin\frac{4\pi~t}{3}$
We can solve the equation for $t$:
$sin\frac{4\pi~t}{3} = 3y$
$\frac{4\pi~t}{3} = arcsin(3y)$
$t = \frac{3}{4\pi}~arcsin(3y)$
Trigonometry (10th Edition)
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
0321671775
ISBN 13:
978-0-32167-177-6
Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.4 Equations Involving Inverse Trigonometric Functions - 6.4 Exercises - Page 282: 53a
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