Angles

Notes:

An angle in ‘standard’ position has its initial side on the positive x-axis and vertex at the origin point, (0,0).

Converting between degrees and radians: If the units of an angle is not specified, they’re assumed to be in radians.

  • π radians = 180˚

  • (π / 2) = 90˚

  • (π / 3) = 60˚

  • (π / 4) = 45˚

  • (π / 6) = 30˚

Formulas / Terms

Angles:

  • Radian Measure: The radian measure of an angle is the length of the arc on the Unit Circle subtended (cut off) by the angle.

  • Degree Measure:

    • 360˚ is a complete revolution
    • 180˚ is a straight angle
    • 90˚ is a right angle
    • 0˚ ≤ Angles ≤ 90˚ are called acute angles
    • 90˚ < Angles are called obtuse angles.

Coterminal Angles: Angles in ‘standard’ position that have the same ‘initial side’ as well as the same ‘terminal side’ are called ‘Coterminal angles’.

Example:

Find four angles that are coterminal with the angle ø = 160˚.

160˚ + 360˚ = 520˚
160˚ + 2(360˚) = 880˚
160˚ - 360˚ = -200˚
160˚ - 2(360˚) = -560˚

To find the length of a circular arc inside of a circle, you can use two equations:

  • S = (t / 2π)(2π * r)

    • First part of the equation (t / 2π): Fraction of whole circle.

    • Second part of the equation (2π * r): Whole circumference.

  • S = t * r

    • Note: This equation only applies if ‘t’ is in radians.

To find the area of a sector use the formula:

  • A = (1 / 2)tr2