WARM UP
1. What do complementary angles add to?
2. What do supplementary angles add to?
3. Find a the complementary angle and
supplementary angle to 60 degrees
Math IV Lesson 19
Essential Question: What is a coterminal angle/
How can I find coterminal angles? How can I find
complements and supplements of degrees in
radians?
Standard: MM4A2. Students will use the circle to
define the trigonometric functions.
a. Define and understand angles measured in
degrees and radians, including but not limited to 0°,
30°, 45°, 60°, 90°, their multiples, and equivalences

 coterminal angles- angles that have the same
terminal ray
270 degrees and -90 degrees
are coterminal angles
 Angles that have the same initial and terminal side.
See the examples below.
Determine 2 coterminal angles, one
positive and one negative for a 60
degree angle.
60 
60 + 360 = 420 degrees
60 – 360 = -300 degrees
HOW TO FIND A COTERMINAL ANGLE?
Add or subtract 360 from any degree
 Add or subtract 2∏ from any radian

Example- Find one positive and one negative
coterminal angle for each of the following
 35 degrees
 ∏/6

SQUIRREL
Example : Determine two co-terminal angles
(one positive and one negative) for the angle 7π/6.
Example : Find the complement and supplement of the angle π/12
More examples
Find a coterminal angle for the following
• 3∏/2
• 320 degrees
Let's say we have an angle β = 600
degrees
360 degrees is once
around
then we have 270
degrees left to go
This puts us in Q3
coterminal angles
600 degrees
240 degrees
-120 degrees
960 degrees
You add or subtract 360 to
get a coterminal angle
Complementary Angles
Sum of the angles is 90
Find the complement of each angles:
40
40 + x = 90
x = 50 degrees
120
No Complement!
Finding complementary angles
Complementary angles add to 90 degrees or add
to ∏/2
Find an angle complementary to ∏/4
Find an angle complementary to 30 degrees
Supplementary Angles
Sum of the angles is 180
Find the supplement of each angles:
40
120
40 + x = 180
120 + x = 180
x = 140 degrees
x = 60 degrees
Supplementary angles
• Supplementary angles add to 180 degrees or
2∏
• Find angles supplementary to the following
45 degrees
∏/6
Radians
3
radians
4

4
radians
3.14 rad 
5
radians
4
6.28 rad 
7
radians
4
Arc measure = central angle
measure
Classwork / homework


Pick 5 from each section on the worksheet to solve
P266 # 31-38