If cos x = - \(\frac{5}{13}\) where 180° < X < 270°, what is the...

If cos x = - \(\frac{5}{13}\) where 180° < X < 270°, what is the value of tan x -sin x ?

A. \(\frac{111}{13}\)
B. \(\frac{321}{65}\)
C. -\(\frac{216}{65}\)
D. \(\frac{112}{13}\)
E. \(\frac{131}{65}\)

Given cos x = - \(\frac{5}{13}\)

→ adj = -5, hyp = 13

Pythagoras' rule → hyp\(^2\) = Opp\(^2\) + adj\(^2\)

Opp\(^2\) = 13\(^2\) - [-5]\(^2\) → 169 - 25

Opp = √144 → 12

tan x = \(\frac{opp}{adj}\) → - \(\frac{12}{5}\)

sin x = \(\frac{opp}{hyp}\) → \(\frac{12}{13}\)

; tan x - sin x → - \(\frac{12}{5}\) - \(\frac{12}{13}\)

= - \(\frac{216}{65}\)

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