Convert each radian measure to degrees. See Examples 2(a) and 2(b). 11π/30

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Understand that to convert radians to degrees, you use the conversion factor \( \frac{180}{\pi} \).

Multiply the given radian measure \( \frac{11\pi}{30} \) by \( \frac{180}{\pi} \).

Set up the multiplication: \( \frac{11\pi}{30} \times \frac{180}{\pi} \).

Notice that the \( \pi \) in the numerator and denominator will cancel each other out.

Simplify the expression by multiplying \( 11 \times 180 \) and then dividing by 30 to find the degree measure.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Radian Measure

A radian is a unit of angular measure used in mathematics. It is defined as the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle. One complete revolution around a circle is equal to 2π radians, making it a fundamental concept in trigonometry and calculus.

Degree Measure

Degrees are another unit of angular measure, where one complete revolution is divided into 360 equal parts. This system is more intuitive for many applications, such as navigation and geometry. To convert radians to degrees, the formula used is: degrees = radians × (180/π).

Conversion Between Radians and Degrees

Converting between radians and degrees is essential in trigonometry, especially when working with trigonometric functions that may require angles in a specific unit. The conversion involves multiplying the radian measure by 180/π to obtain the equivalent degree measure. Understanding this conversion is crucial for solving problems that involve angular measurements.

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