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 radians to degrees.53

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.