On the unit circle, if the terminal point is at $(x,y)$, how many radius lengths is it to the right of the circle's vertical diameter?

• A. $x$
• B. $\sqrt{1}$
• C. $0$
• D. $y$

Answer: (A)

Verified step by step guidance

1. Recall that the unit circle is a circle with radius 1 centered at the origin (0,0) on the coordinate plane.
2. The vertical diameter of the circle is the line x = 0, which divides the circle into left and right halves.
3. The terminal point on the unit circle is given as (x, y), where x and y satisfy the equation of the unit circle: \(x^2 + y^2 = 1\).
4. The distance from the vertical diameter (x=0) to the point (x, y) along the horizontal axis is simply the absolute value of the x-coordinate, which tells us how far right or left the point is from the vertical diameter.
5. Since the radius of the unit circle is 1, the distance to the right of the vertical diameter in terms of radius lengths is exactly \(x\) (assuming \(x\) is positive for right side), so the answer is \(x\).