​ The point P=(x,1/2 ) lies on the unit circle shown below. What is the value of x x in simplest form?

The answer is below

Step-by-step explanation:

A unit circle is a circle on the coordinate plane with a radius of 1 unit. The unit circle center usually lies on the origin.

The equation of a circle is given as:

(x - h)² + (y - k)² = r²

Where (h, k) is the center of the circle and r is the radius of the circle.

As seen in the diagram attached, the center of the circle is at the origin (0, 0) and the circle is a unit circle with a radius of 1. Hence:

(x - h)² + (y - k)² = r²

(x - 0)² + (y - 0)² = 1²

x² + y² = 1

Given the point P(x, 1/2) lies on the circle. To find x, substitute y = 1/2:

x² + (1/2)² = 1

x² + 1/4 = 1

x² = 1 - 1/4 = 3/4

x² = 3/4

x = √(3/4)

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step-by-step explanation: