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 (11th Edition) Clone
by Lial, Margaret L.; Hornsby, John; Schneider, David I.; Daniels, Callie
Published by
Pearson
ISBN 10:
978-0-13-421743-7
ISBN 13:
978-0-13421-743-7
Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.4 Equations Involving Inverse Trigonometric Functions - 6.4 Exercises - Page 288: 55a
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