Question

major arc cbd measures 300°. which is the radian measure of its corresponding central angle?
\\( \frac { 5 \pi } { 6 } \\) radians
\\( \frac { 4 \pi } { 3 } \\) radians
\\( \frac { 11 \pi } { 6 } \\) radians
\\( \frac { 5 \pi } { 3 } \\) radians

Explanation:

Step1: Convert degrees to radians

To convert degrees to radians, use the formula: \( \text{Radians} = \frac{\pi}{180}\times\text{Degrees} \).
Given the angle in degrees is \(300^{\circ}\).
Substitute into the formula: \( \text{Radians}=\frac{\pi}{180}\times300\).

Step2: Simplify the expression

Simplify \( \frac{\pi}{180}\times300=\frac{300\pi}{180}\).
Divide numerator and denominator by \(60\): \( \frac{300\pi\div60}{180\div60}=\frac{5\pi}{3}\).

Answer:

\(\frac{5\pi}{3}\) radians