1. 7.1 – Measurement of Angles
Objectives: You should be able to…
1. Convert radians to degrees and
vice-versa.
2. Find co-terminal angles.

2. *In trigonometry, an angle often represents a rotation about a point.
360 degrees in one revolution.

3. Radian Measure of a Central Angle
the number of radius units in the length of its intercepted arc.

4. Examples: Give the radian measure of θ if: r = 5 and s = 9
b. r = 8 and s = 10

5. *Note: One revolution: degrees = 360° radians = 2π 1 radian =

6. Examples: Convert 240˚ to radians. (nearest hundredth)
Convert 1.7 radians to degrees. (tenth)
c. Convert radians to degrees.

7. Degrees, minutes/seconds
Ex. Convert 12.3º to degrees, min./sec.
Ex. Convert 95º10’ to radians.

8. 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.

9. 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.

10. Example:
Find two angles, one positive and one negative, that are coterminal with the following angles.
56° b.

11. Example: A gear revolves at 40 rpm.
Find the # of degrees per minute through which the gear turns.
b. Find the approximate # of radians
per minute.