Question

The point P is on the unit circle. If the y-coordinate of P is -4/5 and P is in quadrant III , then x = ?

Answer 1

`-3/5`

Explanation:

In a unit circle:

X-Coordinate`=cosx`
Y-Coordinate`=sinx`

If `sinx=-4/5,` the hypotenuse is `1` and the opposite leg is `-4/5`. thus, the other leg is `+-sqrt(1^2-(4/5)^2)=+-sqrt(1-16/25)=+-sqrt(9/25)=+-3/5`

Then, the adjacent leg is `+-3/5`

X-Coordinate`=cosx=+-(3/5)/1=+-3/5`

Since it is in the third quadrant, both x and y are negative. Then, `cosx` is negative, or `-3/5`