If sin x = \(\frac{5}{13}\) and 0 o \(\leq\) x \(\leq\) 90 o , find
MATHEMATICS
WAEC 2013
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. \(\frac{79}{156}\)
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 = \(\frac{12}{13} - \frac{5}{12}\)
\(\frac{144 - 65}{156} = \frac{79}{156}\)
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