Given sin A = 5 / sqrt{89} ​and that angle A is in Quadrant I, find the exact value of cotA in simplest radical form using a rational denominator.

Answer 1

sin(A) = opposite/hypotenuse = 5/√89

cot(A) = adjacent/opposite = √(√89)²-5²)/5 = √(89-25)/5 = √(64)/5 = 8/5

Construct a right triangle with the side opposite of angle A measured to be 5 units and the hypotenuse √89 units. The adjacent side is calculated by doing √(hypotenuse²-opposite²) thanks to the Pythagorean Theorem. cot(A) can then be determined knowing adjacent/opposite.

Therefore, cot(A) = 8/5

Hope this helped!

Answer 2

First determine cosine A using Pythagores

Second determine cot A using cos A / sin A

Third rationalize any denominator