Answer
$x=arcsin(\frac{y+4}{2})$
Work Step by Step
$y=2sinx-4$
$y+4=2sinx$
Divide both sides by 2.
$sinx=\frac{y+4}{2}$
Apply definition of arcsine.
$x=arcsin(\frac{y+4}{2})$
Hence, $x=arcsin(\frac{y+4}{2})$
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 280: 19
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