Answer
(a) $sin~2u=-\frac{24}{25}$
(b) $cos~2u=\frac{7}{25}$
(c) $tan~2u=-\frac{24}{7}$
Work Step by Step
$cos^2u+sin^2u=1$
$cos^2u+(-\frac{3}{5})^2=1$
$cos^2u=1-\frac{9}{25}=\frac{16}{25}$
$cos~u=+\frac{4}{5}~~~~$ ($\frac{3\pi}{2}\lt u\lt2\pi$)
$tan~u=\frac{sin~u}{cos~u}=\frac{-\frac{3}{5}}{\frac{4}{5}}=-\frac{3}{4}$
(a) $sin~2u=2~sin~u~cos~u=2(-\frac{3}{5})(\frac{4}{5})=-\frac{24}{25}$
(b) $cos~2u=cos^2u-sin^2u=\frac{16}{25}-\frac{9}{25}=\frac{7}{25}$
(c) $tan~2u=\frac{2~tan~u}{1-tan^2u}=\frac{2(-\frac{3}{4})}{1-(-\frac{3}{4})^2}=\frac{-\frac{3}{2}}{\frac{7}{16}}=-\frac{24}{7}$
