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. \(\frac{131}{65}\)
Correct Answer:
Explanation
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 → - \(\frac{12}{5}\) - \(\frac{12}{13}\)
= - \(\frac{216}{65}\)
