Question

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

Answer 1

Answer:

$y=+\frac{2\sqrt{2} }{3}$

Step-by-step 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:

$(\frac{1}{3} )^{2} +y^{2} =1\\\\\frac{1+9y^{2} }{9}=\frac{9}{9} \\\\y^{2} =\frac{8}{9} \\\\\sqrt{y^{2}} =\sqrt{\frac{8}{9}}\\\\y=+\frac{2\sqrt{2} }{3}$

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