Angle Measurement: Degrees and Radians
When we work with angles, we need to understand how they're formed and measured. An angle has an initial side and a terminal side that rotates from the initial position, typically counterclockwise for positive angles. The point where these sides meet is called the vertex.
There are two main ways to measure angles. Degrees divide a complete circle into 360 equal parts, while radians use the radius of a circle to measure rotation with a complete circle being 2π radians. Both systems are important in different contexts.
Converting between these systems is straightforward. To convert degrees to radians, multiply by π/180. For example, -45° × π/180 = -π/4 radians. To convert radians to degrees, multiply by 180/π. Remember that negative angles rotate in the clockwise direction!
Pro Tip: When working with common angles, try to memorize both the degree and radian measures of 30°, 45°, 60°, 90°, and 180° to save time on tests and homework.
