Multiple Choice
If the measure of central angle RST is radians in a circle of radius , what is the area of the shaded sector formed by this angle?
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1. Measuring Angles
Radians
Multiple Choice
If arc AB is one-fourth of the circumference of a circle, what is the radian measure of the central angle subtended by arc AB?
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Verified step by step guidance1
Recall that the circumference of a circle is given by the formula \(C = 2 \\pi r\), where \(r\) is the radius of the circle.
Understand that the central angle in radians corresponding to an arc length \(s\) on a circle of radius \(r\) is given by \(\theta = \frac{s}{r}\).
Since arc AB is one-fourth of the circumference, express the arc length as \(s = \frac{1}{4} \times 2 \\pi r = \frac{1}{2} \\pi r\).
Substitute the arc length \(s = \frac{1}{2} \\pi r\) into the central angle formula \(\theta = \frac{s}{r}\) to get \(\theta = \frac{\frac{1}{2} \\pi r}{r}\).
Simplify the expression by canceling \(r\) to find the radian measure of the central angle: \(\theta = \frac{1}{2} \\pi\) radians.
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