The exact measure of the angle is 45°.
How to get the angle?
We know that the terminal side passes through a point of the form (√2/2, y).
Notice that the point is on the unit circle, so its module must be equal to 1, so we can write:
[tex]1 = \sqrt{( \frac{\sqrt{2} }{2} )^2 + y^2} \\\\1^2 = \frac{2}{4} + y^2\\1 - 1/2 = y^2\\\\1/\sqrt{2} = y[/tex]
We know that y is positive because the point is on the first quadrant.
Now, we know that our point is:
(√2/2, 1/√2)
And we can rewrite:
√2/2 = 1/√2
So the point is:
( 1/√2, 1/√2)
Finally, remember that a point (x, y), the angle that represents it is given by:
θ = Atan(y/x).
Then in this case, we have:
θ = Atan(1/√2/1/√2) = Atan(1) = 45°
If you want to learn more about angles, you can read:
https://brainly.com/question/17972372
