Mathematics

If cos θ = 5/13, what is the value of tan (theta) for 0 

If cos θ = 5/13, what is the value of tan (theta) for 0 < θ < 90° ?

  • A.
    13
  • B.
    5
  • C.
    13/5
  • D.
    12/5
  • E.
    5/12
Correct Answer: Option D
Explanation

(cos theta = frac{5}{13})

(implies) In the right- angled triangle, with an angle (theta), the adjacent side to (theta) = 5 and the hypotenuse = 13.

(therefore 13^2 = opp^2 + 5^2)

(opp^2 = 169 – 25 = 144 implies opp = sqrt{144})

= 12.

(tan theta = frac{opp}{adj} = frac{12}{5})