Question

Given a unit circle, what is the
value for y?
(1/3, y)
y = ?

Answer 1

`y=+(2√(2) )/(3)\\`

Explanation:

In the unit circle we have:

`x^(2) +y^(2) =1`

In the picture we see that x=1/3.

Using de equation of unit circle:

`((1)/(3) )^(2) +y^(2) =1\\\\(1+9y^(2) )/(9)=(9)/(9) \\\\y^(2) =(8)/(9) \\\\\sqrt{y^(2)} =\sqrt{(8)/(9)}\\\\y=+(2√(2) )/(3)`

y is positive because y are in the first quadrant of the cartesian plane.