Given that tan x = 5/12, what is the value of sin x + cos x ?
A
5/13
B
7/13
C
12/13
D
17/13
E
5/12
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\tan x = \frac{opp}{adj} = \frac{5}{12}\)
\(Hyp^2 = opp^2 + adj^2\)
\(Hyp^2 = 5^2 + 12^2\)
= \(25 + 144 = 169\)
\(Hyp = \sqrt{169} = 13\)
\(\sin x = \frac{5}{13}; \cos x = \frac{12}{13}\)
\(\sin x + \cos x = \frac{5}{13} + \frac{12}{13}\)
= \(\frac{17}{13}\)
Source: Myschool Past Questions Archive (Record #23217)