If tan x = \(\frac{4}{3}\), 0\(^o\) < x < 90\(^o\), find the value of sin x - cos x
A
\(\frac{1}{10}\)
B
\(\frac{1}{5}\)
C
\(\frac{5}{12}\)
D
1\(\frac{2}{5}\)
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
From the diagram,
h\(^2\) = 4\(^2\) + 3\(^2\) (pythagoras')
h\(^2\) = 16 + 9 = 25
h = \(\sqrt{25}\) = 5
Hence, sin x - cos x
= \(\frac{4}{5} - \frac{3}{5}\)
= \(\frac{1}{5}\)
Source: Myschool Past Questions Archive (Record #49606)