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
\(\frac{209}{156}\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
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 = \(\frac{12}{13} - \frac{5}{12}\)
\(\frac{144 - 65}{156} = \frac{79}{156}\)
Source: Myschool Past Questions Archive (Record #36876)