This document discusses trigonometry and angles. It defines angles in degrees and radians, and coterminal angles. Degrees can be divided into minutes and seconds. One radian is defined as the central angle whose arc length equals the radius. Conversions between degrees and radians are provided. Coterminal angles have the same terminal ray but different measures. Examples are given to find coterminal angles of π/4 and 4π/3.

1. Objectives:
1. Measure angles in degrees and radians
2. Find coterminal angles

2.  Trigonometry
comes from Greek
words meaning “triangle
measurement.”
 Has been used for centuries in
navigation and surveying.

3.  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

4.  Examples:
12.3 = 12 + 0.3(60)’ = 12 18’

5.  Convert
 200
40’
to a decimal:

6.  One
radian is the measure of a
central angle whose arc length is
equal to the radius.

7. A
central angle θ (in radians) is:
where s = arc length and r = radius
 Also,
s = rθ

8. 1
revolution = 360 = 2π radians
 ½ revolution = 180 = π radians
 To
convert:

9.  Convert
 Convert
-220 to radians (π).
to degrees.

10.  Convert
 Convert
196 to radians (decimal).
1.35 radians to decimal
degrees.

12.  Vertex
at origin
 Initial ray on + x-axis
 Counterclockwise rotation is +
 Clockwise rotation is -

13.  Two
angles in std. position are
coterminal if they have the same
terminal ray.
 Each angle has infinitely many
coterminal angles.

14.  Find
two angles, one + and one -,
that are coterminal with π/4. Sketch
all 3 angles.

15.  Find
two (+ and -) coterminal angles
of 4π/3.