URGENT- Please help

Question

Given cot A=4/9​ and that angle A is in Quadrant III, find the exact value of sin A in simplest radical form using a rational denominator.

Answer 1

If in Q3, both sin and cos are negative.

cot A = -4/-9 = x/y

Hypotenuse, h = √(x²+y²) = √(16+81) = √97

sin A = y/h = -9/√97 = -(9√97)/97

Answer 2

Given cot A=4/9​ and that angle A is in Quadrant III, find the exact value of sin A in simplest radical form using a rational denominator.

EASY...

since cot = cos / sin or x / y or adj / opp

cot A = 4 / 9 implies that in the 3rd quadrant both x and y are negative

So adjacent to angle A is the x axis at -4

And, Opposite of angle A is the y-axis at -9

thus.. the sin A = opp / hyp

the hypotenuse is deduces using the pythagorean theorem... why not?

(-4)² + (-9)² = hyp²

hyp = √97

and the Sin A = -9/√97

The denominator can be rationalized by multiplying by √97 top and bottom to yield:

-9√97/97