What is the radius of a unit circle?

What is the radius of a unit circle?

• A. 0
• B. 1
• C. π
• D. 2

Answer: (B)

The radius of a unit circle is defined to be 1. A unit circle is a circle with a center at the origin (0, 0) in a coordinate plane and a radius of exactly one unit. This means that every point on the circumference of the circle is one unit away from the center. The concept of a unit circle is fundamental in trigonometry, as it helps relate angles to coordinates on the circle corresponding to various angles measured in radians or degrees. The other options represent values that do not correspond to the radius of a unit circle: - A radius of 0 would imply a point rather than a circle, as a circle cannot exist without a specific nonzero radius. - π, which is approximately 3.14, does not describe any radius of a unit circle. - A radius of 2 indicates a circle larger than a unit circle and would not fulfill the definition of a unit circle. Therefore, the radius of the unit circle being 1 is consistent with its basic definition in geometry and trigonometry.

The radius of a unit circle is defined to be 1. A unit circle is a circle with a center at the origin (0, 0) in a coordinate plane and a radius of exactly one unit. This means that every point on the circumference of the circle is one unit away from the center. The concept of a unit circle is fundamental in trigonometry, as it helps relate angles to coordinates on the circle corresponding to various angles measured in radians or degrees.

The other options represent values that do not correspond to the radius of a unit circle:

• A radius of 0 would imply a point rather than a circle, as a circle cannot exist without a specific nonzero radius.

• π, which is approximately 3.14, does not describe any radius of a unit circle.

• A radius of 2 indicates a circle larger than a unit circle and would not fulfill the definition of a unit circle.

Therefore, the radius of the unit circle being 1 is consistent with its basic definition in geometry and trigonometry.