Chapter 7 - Section 7.3 - Double-Angle, Half-Angle, and Product-Sum Formulas - 7.3 Exercises - Page 561: 9

$sin2x=-\frac{3}{5}$ $cos2x=\frac{4}{5}$ $tan2x=-\frac{3}{4}$

Given $tan(x)=-\frac{1}{3}$ and $cos(x)\gt0$, we have $sin(x)=-\frac{\sqrt {10}}{10},cos(x)=\frac{3\sqrt {10}}{10}$ $sin2x=2sin(x)cos(x)=-\frac{3}{5}$ $cos2x=2cos^2x-1=\frac{4}{5}$ $tan2x=\frac{sin2x}{cos2x}=-\frac{3}{4}$