Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.4 Equations Involving Inverse Trigonometric Functions - 6.4 Exercises - Page 281: 51a

$t = \frac{1}{2\pi~f}~arcsin(\frac{E}{E_{max}})$

$E = E_{max}~sin~(2\pi~f~t)$ We can solve this equation for $t$: $sin~(2\pi~f~t) = \frac{E}{E_{max}}$ $2\pi~f~t = arcsin(\frac{E}{E_{max}})$ $t = \frac{1}{2\pi~f}~arcsin(\frac{E}{E_{max}})$