Convert each radian measure to degrees. See Examples 2(a) and 2(b). ―7π/20

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Identify the conversion factor between radians and degrees, which is \( \frac{180^\circ}{\pi} \).

Multiply the given radian measure by the conversion factor: \( -\frac{7\pi}{20} \times \frac{180^\circ}{\pi} \).

Cancel out \( \pi \) in the numerator and denominator.

Simplify the expression by multiplying \( -\frac{7}{20} \) by \( 180^\circ \).

Calculate the resulting 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

Radian measure is a way of measuring angles based on the radius of a circle. One radian is the angle formed when the arc length is equal to the radius of the circle. This unit is essential in trigonometry as it relates directly to the properties of circles and periodic functions.

Degree Measure

Degree measure is another unit for measuring angles, where a full circle is divided into 360 equal parts. Each part is called a degree. Understanding the conversion between radians and degrees is crucial for solving problems in trigonometry, as many functions and equations are often expressed in one of these units.

Conversion Formula

To convert radians to degrees, the formula used is: degrees = radians × (180/π). This formula allows for the straightforward transformation of angle measures, facilitating the use of trigonometric functions that may require angles in degrees rather than radians.

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