Mathematics

Given that tan x = 5/12, what is the value of sin x + cos…

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})