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
Correct Answer: Option 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})