One of Sin X, Cos X, and Tan X Is $$\sin x = \frac { 12 } { 13 } , \quad x \text { in } \left[ \frac { \pi } { 2 } , \pi \right]$$

Multiple Choice

One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.
- $$\sin x = \frac { 12 } { 13 } , \quad x \text { in } \left[ \frac { \pi } { 2 } , \pi \right]$$

A) $\cos x = \frac { 5 } { 13 } , \tan x = \frac { 12 } { 5 }$
B) $\cos x = - \frac { 5 } { 13 } , \tan x = - \frac { 5 } { 12 }$
C) $\cos x = - \frac { 5 } { 13 } , \tan x = - \frac { 12 } { 5 }$
D) $\cos x = \frac { 5 } { 13 } , \tan x = - \frac { 5 } { 12 }$