Angles and their measures (radians/degrees) An angle is the angle formed between two rays of a line. It is commonly measured in both radians and degrees, ea...
Angles and their measures (radians/degrees)
An angle is the angle formed between two rays of a line. It is commonly measured in both radians and degrees, each with its own unique conversion factors.
Radians: A radian is the angle that is formed when the arc length of the radius of a circle is equal to the length of the arc. The circumference of a circle is equal to 2πr, where r is the radius of the circle. Therefore, a radian is equal to 2π/360 degrees.
Degrees: A degree is the angle that is formed when the arc length of the minute hand of a clock is equal to the length of the hour hand. There are 60 degrees in a circle, so a degree is equal to 1/60 of a radian.
Conversion between radians and degrees:
1 radian = π/180 degrees
1 degree = π/180 radians
Examples:
An angle that measures 30 degrees is equal to 0.5 radians.
The angle formed by the arc length of the radius of a circle with a radius of 5 cm is equal to 10 radians.
The angle formed by the arc length of the minute hand of a clock with a period of 60 s is equal to π/60 radians