Question

What is the x-coordinate of the point where the 45-45-90 triangle in this image intersects the unit circle?

(1 point)
The x-coordinate is
.

Be sure to rationalize the denominator.

Answer 1

For a 45° angle on the unit circle x = y, so 2x^2 = 1 ⇒ x^2 = 1/2 ⇒ x = 1/√2. Rationalizing the denominator gives x = √2/2.