Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.4 Equations Involving Inverse Trigonometric Functions - 6.4 Exercises - Page 282: 53b

$t = 0.27~s$

$y = \frac{1}{3}sin\frac{4\pi~t}{3}$ We can find $t$ when $y = 0.3$: $\frac{1}{3}sin\frac{4\pi~t}{3} = 0.3$ $sin\frac{4\pi~t}{3} = 0.9$ $\frac{4\pi~t}{3} = arcsin(0.9)$ $t = \frac{3}{4\pi}~arcsin(0.9)$ $t = \frac{3}{4\pi}~(1.12)$ $t = 0.27~s$