Angle Conversion: Degrees to Radians Made Easy

TLDR; Converting angles from degrees to radians involves multiplying by a unit fraction. The process simplifies the angle measure and eliminates the units of degrees.

⚙️ Unit Fraction Conversion

To convert angles from degree measure to radian measure, a unit fraction is used.

The unit fraction comes from the equation 2/PI radians is equal to 360 degrees. By dividing both sides of the equation by 360 degrees, a unit fraction of PI/180 degrees is derived.

This unit fraction is crucial for the conversion process.

Alternatively, dividing both sides of the equation by 2/PI radians yields the unit fraction 180 degrees/PI.

Understanding and utilizing these unit fractions is essential for the conversion process.

Determining which unit fraction to use for the conversion involves thinking of the degree measure as a fraction.

By simplifying out the degree measure, the appropriate unit fraction can be identified for converting from degrees to radians.

⏩ Conversion Process

The conversion process from degrees to radians involves multiplying the angle by PI/180 degrees and then simplifying.

For example, when converting 135 degrees to radians, the common factor of 45 simplifies the angle to 3PI/4 radians.

Similar steps are applied to other examples, such as converting 60 degrees to -1PI/3 radians and 15 degrees to PI/12 radians.

Each example demonstrates the process of simplifying the angle measure and eliminating the units of degrees to obtain the angle in radians.

⚖️ Simplification and Result

After applying the conversion process to various angle measures, the common factors, such as 12, 15, and 45, are used to simplify the angles from degrees to radians.

For instance, 48 degrees simplifies to -4PI/15 radians.

The final result of each conversion demonstrates the angle measure in radians, achieved through the simplification process using the appropriate unit fraction and common factors.