Given cos ⁡ A = 5 /11 and that angle A is in Quadrant I, find the exact value of cot ⁡A in simplest radical form using a rational denominator.

Answer 1

sin A = 5√3 / 11 by Pythagoras

cot A = [5 / 11] / [5√3 / 11]

cot A = [5 / 11][11/ 5√3]

cot A = 1 / √3

You can rationalize the denominator.

Answer 2

Cos A = 5/11 where 5 is the horizontal component and 11 is the hypotenuse,

yields the vertical component of the triangle as √(11² - 5²) = √96 = 4√6