Question

Convert from radians to degrees. $$ \frac{19 \pi}{20} $$

   Convert from radians to degrees.
$$
\frac{19 \pi}{20}
$$

Algebra and Trigonometry

Algebra and Trigonometry

Cynthia Y. Young 4th Edition

Chapter 6, Problem 39

Instant Answer

Solved by Expert Dharmendra Jain

06/21/2021

Step 1

Step 1: First, we recall the conversion factor between radians and degrees, which is $\pi$ radians = 180 degrees. Show more…

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Convert from radians to degrees. $$ \frac{19 \pi}{20} $$

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Key Concepts

Radians

Radians are the standard unit of angular measure used in mathematics and physics, defined by the relationship between the length of an arc and the radius of a circle. They provide a natural way of relating the geometry of circles with algebra and calculus, making them essential for trigonometric and periodic function analysis.

Degrees

Degrees are another unit of angular measure where a full circle is divided into 360 equal parts. They are widely used in many fields due to their intuitive nature, such as in navigation, geography, and everyday understanding of angles.

Conversion Factor

The conversion factor between radians and degrees is critical in relating the two measurement systems. Since ? radians are equivalent to 180 degrees, the conversion from radians to degrees involves multiplying the radian value by 180/?, allowing for seamless transitions between the mathematical and applied interpretations of angles.

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