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If cos x = - $\frac{5}{13}$ where 180° < X < 270...

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.

$\frac{131}{65}$

View answer & explanation

Correct answer is C

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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