Radians to Degrees Conversion Worksheet: Answers & Solutions

When working with angles in mathematics, it's common to encounter degrees and radians, two systems of units that measure angles differently. To interchange between these two systems, a clear understanding and conversion between degrees to radians and radians to degrees is crucial. This article will guide you through this process, including sample worksheet answers to aid your understanding.

Before we dive into the conversions, let's ensure we understand the basics. One degree is defined as 1/360th of a complete rotation, while one radian is defined as the angle subtended at the center of a circle by an arc length equal to the radius of the circle. Now, let's move on to the main topics.

Degrees to Radians

To convert degrees to radians, you multiply the angle in degrees by the factor (π/180). This is because there are 180 degrees in π radians.

For instance, if you have an angle of 90 degrees, to convert it to radians, you calculate: 90 * (π/180) = π/2 radians.

Direct Conversion

Using the formula, we can directly convert degrees to radians. For example, 180 degrees equals 2π radians because 180 * (π/180) = π * 2.

Another example, 45 degrees converts to π/4 radians since 45 * (π/180) = π/4.

Inverse Conversions

It's also crucial to practice converting from a radian angle to its equivalent in degrees. To do this, divide the angle in radians by (π/180).

For example, converting π/3 radians to degrees: (π/3) / (π/180) = 60 degrees.

Radians to Degrees

To convert radians to degrees, you multiply the angle in radians by the factor (180/π). This is the reciprocal of the conversion from degrees to radians.

For instance, to convert 3 radians to degrees, you calculate: 3 * (180/π) ≈ 171.89 degrees.

Conversions with Quadratic Radians

It's not uncommon to encounter angles that are in terms of π. To convert these radians to degrees, directly apply the formula: π * (180/π) = 180 degrees.

For example, if you need to convert π/4 radians to degrees, it directly converts to 45 degrees because π/4 * (180/π) = 45.

Approximating with PI Value

Since π is an irrational number, we often use an approximation (like 3.14) in conversions. For instance, converting 2 radians to degrees using the approximation π ≈ 3.14: 2 * (180/3.14) ≈ 114.59 degrees.

Please ensure you're using the correct decimal places when approximating π for precision.

In the journey of mastering these conversions, practicing with worksheets is invaluable. It builds your understanding and familiarity with these conversions. Here are a few worksheet answers to aid your learning:

Degrees	Radians
45	π/4
60	π/3
180	π

Now, extend your learning by tackling these conversions in reverse, and always double-check your work. As you progress in your mathematical journey, you'll find these conversions becoming second nature, opening doors to understanding more complex trigonometric concepts.