Question

the point P = (x, -5/7) lies on the unit curcle shown below. What is the value of x in the simplest form?

Answer 1

Answer:

$x =\± \frac{2\sqrt{6}}{7}$

Step-by-step explanation:

The question has missing details as the unit circle is not shown, However, I'll solve on a general terms.

Given

$P = (x,-\frac{5}{7})$

Required

Determine the possible value of x

Since point p lies on the unit circle, we'll solve this question using the following unit circle formula:

$x^2 + y^2 = 1$

Substitute -5/7 for y

$x^2 + (-\frac{5}{7})^2 = 1$

$x^2 + \frac{25}{49} = 1$

Collect Like Terms

$x^2 =1- \frac{25}{49}$

Take LCM

$x^2 =\frac{49 -25}{49}$

$x^2 =\frac{24}{49}$

Take the square root of both sides

$x =\± \sqrt{\frac{24}{49}}$

$x = \±\frac{\sqrt{24}}{7}$

$x = \±\frac{\sqrt{4*6}}{7}$

Split

$x = \±\frac{\sqrt{4}*\sqrt{6}}{7}$

$x =\± \frac{2*\sqrt{6}}{7}$

$x =\± \frac{2\sqrt{6}}{7}$