Question

What is cos fata if sin fata= -8/10 and fata is in Quadrant 3?​

Answer 1

Explanation:

First thing is to remember the sin ratio. It is, by definition, the side opposite over the hypotenuse of the reference angle. In QIII the side opposite the angle is -8 which is one of the legs of a right triangle, and the hypotenuse, which is always positive, is 10. That means that if we are going to find the cosine of the angle, we need the other leg of the triangle. Using Pythagorean's Theorem, we find that

`a^2+(-8)^2=10^2` and

`100-64=a^2` and

`a^2=36` so

a = 6. But because we are QIII, that value is negative, because x is negative in QIII.

That leg happens to be the side adjacent to the angle. The cosine of the angle is the side adjacent over the hypotenuse. So now that we have the side adjacent as -6, we can say that the cosine of the angle is -6/10.