If sin x = \(\frac{5}{13}\) and 0o \(\leq\) x \(\leq\) 90o, find the value of (cos x - tan x)
A. \(\frac{7}{13}\) B. \(\frac{12}{13}\) C. \(\frac{79}{156}\) D. \(\frac{209}{156}\)
Correct Answer: C
Explanation
Sin x = \(\frac{5}{13}\) 0o \(\leq\) x \(\leq\) 90o, (cos x - tan x) AC2 = AB2 + BC2 132 = 52 + BC2 169 - 25 + BC2 169 - 25 = BC2 144 = BC2 Cos x = \(\frac{Adj}{Hyp}\) = \(\frac{12}{13}\) BC = \(\sqrt{144}\) BC = 12 tan x = \(\frac{opp}{adj} = \frac{5}{12}\) BC = 12 cos x - tan x = \(\frac{12}{13} - \frac{5}{12}\) \(\frac{144 - 65}{156} = \frac{79}{156}\)
