The point $P ( x , y )$ is on the unit circle in quadrant III. If $x = - \sqrt { 11 } / 6$
Find y
A) $y = \sqrt { 11 } / 6$
B) $y = \sqrt { 5 } / 6$
C) $y = 11 / 6$
D) $y = 5 / 6$
E) $y = - 5 / 6$

Question

Quizplus · Accepted Answer

Since the point is on the unit circle, we know that $x^2 + y^2 = 1$. Substituting $x = -\sqrt{11}/6$ gives $y^2 = 1 - x^2 = 1 - ( -\sqrt{11}/6)^2 = 1 - 11/36 = 25/36$. Taking the square root of both sides and noting that $y$ is negative in quadrant III gives $y = -5/6$. Therefore, the answer is choice E.

The Point P(x,y)P ( x , y )P(x,y) Is on the Unit Circle in Quadrant III

The Point $P ( x , y )$ Is on the Unit Circle in Quadrant III