Answer:
Explanation:
We know that the cosine of an angle is the reciprocal of the secant of the same angle, and the cotangent of an angle is the reciprocal of the tangent of the same angle. Therefore, we can use these relationships to find the value of the secant of an angle when the cotangent of the same angle is given.We are given that cot(o) = 13/6. Using the definition of the cotangent function, we know that:cot(o) = adjacent side / opposite sideWe can use the Pythagorean theorem to find the hypotenuse of a right triangle with adjacent side 13 and opposite side 6:h^2 = 13^2 + 6^2
h^2 = 169 + 36
h^2 = 205
h = sqrt(205)Now we can use the definitions of the secant and cosine functions to find the value of sec(o):sec(o) = hypotenuse / adjacent side
sec(o) = sqrt(205) / 13Therefore, the value of sec(o) is:sec(o) = sqrt(205) / 13 ≈ 1.5276