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 = (3√(5))/(7)\\\\`

Step-by-step 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(-(2)/(7)\right) = 1\\\\x^2+(4)/(49) = 1\\\\x^2 = 1-(4)/(49)\\\\x^2 = (49)/(49)-(4)/(49)\\\\x^2 = (45)/(49)\\\\x = \sqrt{(45)/(49)} \ \ \text{ ... x is positive}\\\\x = (√(45))/(√(49))\\\\x = (√(9*5))/(7)\\\\x = (√(9)*√(5))/(7)\\\\x = (3√(5))/(7)\\\\`