Question

The point P=\left(-\frac{1}{2},\,\, y\right)P=(− 2 1 ​ ,y) lies on the unit circle shown below. What is the value of yy in simplest form? X y (1, 0) P (x, y

Answer 1

Answer:

$y = \frac{\sqrt{3}}{2}}$

Step-by-step explanation:

We are given a point P which lies on a unit circle

P  = (-½, y)

Where x coordinate is -½ and y coordinate is y.

We are asked to find the value of y in simplest form.

Recall that a unit circle has a radius of 1 and is centered at the origin that is (0,0).

The equation of the unit circle is given by

$x^{2} + y^{2} = 1$

Since the point P lies on a unit circle, we can substitute this point into the equation of unit circle and get the value of y.

Substitute x = -½ and y = y

$(-\frac{1}{2} )^{2} + y^{2} = 1\\\\(\frac{1}{4} ) + y^{2} = 1\\\\y^{2} = 1 - \frac{1}{4} \\\\y^{2} = \frac{3}{4} \\\\y = \pm \sqrt{\frac{3}{4}} \\\\y = \pm \frac{\sqrt{3}}{2}}$

Assuming that the given point P lies in the 2nd quadrant, the value of y will be positive.

$y = \frac{\sqrt{3}}{2}}$

Therefore, the coordinates of the point P are

$P =( -\frac{1}{2} , \frac{\sqrt{3}}{2}})$