Chapter 6 - Inverse Circular Functions and Trigonometric Equations - Section 6.4 Equations Involving Inverse Trigonometric Functions - 6.4 Exercises - Page 285: 9

$x=\frac{1}{2}arctan(\frac{y}{3})$

$y=3tan2x$ Need to solve $x$ in order to find this divide the above equation by 3 both sides. $tan2x=\frac{y}{3}$ Now, isolate $x$ as follows: $2x=arctan (\frac{y}{3})$ $x=\frac{1}{2}arctan(\frac{y}{3})$