The point P is on the unit circle. If the y-coordinate of P is − 4/8, and P is in quadrant IV, then x =

Answer 1

So the first step is to reduce the y coordinate to -1/2, next we can use our knowledge of the unit circle to say in Quadrant 4 x is positive and y is negative. Also for one of the Pythagorean identities, the hypotenuse is 1, one side is 1/2, so the other side must be sqrt(3)/2.

That is the memorizing the unit circle method. If you want the mathematical method we say the unit circle hypotenuse is always 1 and the side opposite of the central angle is the y length, so we can say arcsin(-1/2/1)=-30degrees or -pi/6, then we want the x value so we do cos(-30degrees)=cos(-pi/6)=sqrt(3)/2