Given sin A = 12/13 and that angle A is in Quadrant 1,
find the exact value of cot A in simplest radical form
using a rational denominator.

We have been given that and angle A is in quadrant 1. We are asked to find the exact value of in simplest radical form.

We know that sine relates opposite side of right triangle with hypotenuse.

This means that opposite side is 12 units and hypotenuse is 13 units.

We know that cotangent relates adjacent side of right triangle with adjacent side.

Now we will find adjacent side using Pythagoras theorem as:

Let us take positive square root on both sides:

Therefore, adjacent side of angle A is 5 units.

Therefore, the exact value of cot A is .

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step-by-step explanation: