Question

Hello, I can't understand how can you figure out what quadrant does the result of the following exercise belong to. Help welcomed. Thanks.

Question 3: In a triangle ABC, we have that cos Y = 513, what is the values of sin Y?
Solution:
We have the basic trigonometric identity, Sin2 A + cos2 A = 1

In our case, we know cos Y = 513

sin2 Y = 1 - (513)2

sin2 Y = 1 - 25169 = 144169

sin Y = ± 144169‾‾‾‾√ = -1213.

(Because cos Y is +ve, lies in lV quadrant. Value of sin Y is -ve in this quadrant.)