Circular Measure
Conversion between degrees and radians
Some formulas in circular measures require the substitution of angles in radians. It is important to memorize the conversion between degrees and radians. Don’t worry, it’s easy! (refer to the diagram)
Watch the video for a detailed explanation and examples.
Parts of a circle
Know your circle.
There are many parts to a circle, namely:
- Major arc
- Minor arc
- Major sector
- Minor sector
- Segment
- Chord
An arc is simply a part of a circumference. When the circumference of a circle is divided into two parts, the longer part is known as the major arc. The shorter part of the circumference is known as the minor arc.
Just like the arc, a sector is simply part of a circle – think about a slice of pie. When a circle is cut into two parts, the larger part is known as the major sector. The smaller part of the circle is known as the minor sector.
On the other hand, a segment is a specific part of a sector (refer to the diagram).
Formulas
There are several formulas in this topic. It is important to understand when to use angles in degrees and angles in radians.
Whenever an angle is used with a trigonometric ratio (sin θ or sin(θ/2)), it should be in degrees. Normally, your calculator is set to degrees mode. However, if your calculator is set to radian mode, then the angle should be in radian.
Whenever an angle is not used together with a trigonometric ratio, it should always be used in radians.
Watch the video for examples.
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