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