Question

If the terminal side of angle θ passes through a point on the unit circle in the first quadrant where x=√2/2, what is the exact measure of θ?

Answer 1

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:

$1 = \sqrt{( \frac{\sqrt{2} }{2} )^2 + y^2} \\\\1^2 = \frac{2}{4} + y^2\\1 - 1/2 = y^2\\\\1/\sqrt{2} = y$

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:

brainly.com/question/17972372