7.1 – Measurement of
Angles
Objectives: You should be able to…
1. Convert radians to degrees and
vice-versa.
2. Find co-terminal angles.
*In trigonometry, an angle often
represents a rotation about a point.
360 degrees in one revolution.
Radian Measure of a Central Angle
• the number of radius units in the length of its
intercepted arc.
Examples:
• Give the radian measure of θ if:
a. r = 5 and s = 9
b. r = 8 and s = 10
*Note:
• One revolution:
degrees = 360°
radians = 2π
1 radian =
1 degree =
Examples:
a. Convert 240˚ to radians. (nearest hundredth
and exact value)
b. Convert 1.7 radians to degrees. (tenth)
c. Convert
5
3
radians to degrees.
Degrees, minutes/seconds
• 25 degrees, 20 minutes, 6 seconds: 25°20’6”
Ex. Convert 12.3º to degrees, min./sec.
Ex. Convert 95º10’ to radians.
• When an angle is shown in a coordinate plane,
it usually appears in standard position, with its
vertex at the origin and its initial ray along the
positive x-axis.
Coterminal Angles
• 2 angles in standard position, if they have the
same terminal ray.
• There are infinitely many for each terminal ray.
*Add or subtract 360° or 2𝜋 from
original angle.
Example:
• Find two angles, one positive and one
negative, that are coterminal with the
following angles.
a. 56°

b. 6
Example:
• A gear revolves at 40 rpm.
a. Find the # of degrees per minute through
which the gear turns.
b. Find the approximate # of radians
per minute.