Question

The point P = (x, - 2/7) lies on the unit circle shown below. What is the value of x in simplest form?

Answer 1

Answer: $x = \frac{3\sqrt{5}}{7}$

Explanation:

The equation of the unit circle is $x^2+y^2 = 1$

Plug in y = -2/7 and solve for x

$x^2+y^2 = 1\\\\x^2+\left(-\frac{2}{7}\right) = 1\\\\x^2+\frac{4}{49} = 1\\\\x^2 = 1-\frac{4}{49}\\\\x^2 = \frac{49}{49}-\frac{4}{49}\\\\x^2 = \frac{45}{49}\\\\x = \sqrt{\frac{45}{49}} \ \ \text{ ... x is positive}\\\\x = \frac{\sqrt{45}}{\sqrt{49}}\\\\x = \frac{\sqrt{9*5}}{7}\\\\x = \frac{\sqrt{9}*\sqrt{5}}{7}\\\\x = \frac{3\sqrt{5}}{7}$