Objectives:

1. Measure angles in degrees and radians

2. Find coterminal angles

Trigonometry comes from Greek

words meaning “triangle

measurement.”

Has been used for centuries in

navigation and surveying.

In trig, angles represent rotations about a point.

One revolution (complete rotation) contains 360 .

Degrees can be divided into 60 minutes and each minute into 60 seconds.

Example: 25 20’6” is 25 degrees, 20 minutes, and 6 seconds

Examples:

12.3 = 12 + 0.3(60)’ = 12 18’

Convert to a decimal:

200 40’

One radian is the measure of a

central angle whose arc length is

equal to the radius.

A central angle θ (in radians) is:

where s = arc length and r = radius

Also, s = rθ

1 revolution = 360 = 2π radians

½ revolution = 180 = π radians

To convert:

Convert -220 to radians (π).

Convert to degrees.

Convert 196 to radians (decimal).

Convert 1.35 radians to decimal

degrees.

Vertex at origin

Initial ray on + x-axis

Counterclockwise rotation is +

Clockwise rotation is -

Two angles in std. position are

coterminal if they have the same

terminal ray.

Each angle has infinitely many

coterminal angles.

Find two angles, one + and one -,

that are coterminal with π/4. Sketch

all 3 angles.

Find two (+ and -) coterminal angles

of 4π/3.