Educator

Angles

Main definitions and formulas:

• Degrees are a unit of measurement by which a circle is divided into 360 equal parts, denoted 360^° .
• Radians are a unit of measurement by which a circle is divided into 2π parts, denoted 2π ^R.
  • Since the circumference of a circle is 2π r, this means that a 1^R angle cuts off an arc whose length is exactly equal to the radius. (It is [1/(2π )] of the whole circle.)
  • Since 2π ≈ 6.28..., this means that 1^R is about one sixth of a circle. But we seldom use whole numbers of radians. Instead we use multiples of π . For example, (π /2)^R is exactly one fourth of a circle.

• degree measure × π 180 = radian measure

• radian measure × 180 π = degree measure

• Coterminal angles are angles that differ from each other by adding or subtracting multiples of 2π ^R (i.e. 360^° ). If you graph them in the coordinate plane starting at the x-axis, they terminate at the same place.
• Complementary angles add to (π /2)^R(i.e. 90^° ).
• Supplementary angles add to π ^R (i.e. 180^° ).