Question

Cos x=-1/2 x lies in third quadrant what is sin x?

Answer 1

cos x = -1/2 = Base/Hypotenuse. so let Base = 1 and Hypotenuse = 2.
Now by pythagoras theorem.
(Hypotenuse)^{2} = (Perpendicular)^{2} + (Base)^{2}
putting the values of Base an Hypotenuse we get :-
(2)^{2} = (Perpendicular)^{2} + (1)^{2}
4-1 = (Perpendicular)^{2}
3 = (Perpendicular)^{2}
\sqrt{3} = Perpendicular
so the Sin x = \sqrt{3}/2
and since the x lies in third quadrant therefore, sin will be in negative
Hence, Sin x = - \sqrt{3}/2