Given that tan x = 5/12, what is the value of sin x + cos x ?
- 5/13
- 7/13
- 12/13
-
17/13
- 5/12
The correct answer is: D
Explanation
\(\tan x = \frac{opp}{adj} = \frac{5}{12}\)
\(Hyp^2 = opp^2 + adj^2\)
\(Hyp^2 = 5^2 + 12^2\)
= \(25 + 144 = 169\)
\(Hyp = \sqrt{169} = 13\)
\(\sin x = \frac{5}{13}; \cos x = \frac{12}{13}\)
\(\sin x + \cos x = \frac{5}{13} + \frac{12}{13}\)
= \(\frac{17}{13}\)