Why is the Radius Always 1 in a Unit Circle?
Discover why the radius of a unit circle is defined as 1 unit, simplifying many mathematical calculations.
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If 'radius' always being 1 refers to a unit circle in mathematics, it is because a unit circle is defined as a circle with a radius of 1 unit. This circle is centered at the origin (0,0) in the coordinate plane and simplifies many trigonometric calculations.
FAQs & Answers
- What is a unit circle? A unit circle is a circle with a radius of 1 unit, centered at the origin (0,0) on the coordinate plane.
- Why is the unit circle important in trigonometry? The unit circle simplifies the calculation of sine, cosine, and tangent values for various angles, making it fundamental in trigonometry.
- How do you calculate the circumference of a unit circle? The circumference of a unit circle is calculated using the formula C = 2πr, where r is the radius. With r as 1, the circumference is 2π.
- Can the radius of a circle be any value? Yes, a circle can have any radius. However, a unit circle specifically has a radius of 1.