1. Table of Contents 2. Angles and their Measures - continued

2. Angles and their Measures - continued Essential question – What are other operations to be done for angles?

3. What quadrant is it in? To find out what quadrant an angle is in
Make a negative angle positive by adding 360o or 2π (may need to do multiple times)
If angle is bigger than 360o or 2π, make it smaller by subtracting 360o or 2π (may need to do multiple times)
Figure out what quadrant it is in based on angles of axes (from yesterday)
If the question asks you to sketch the angle,
draw the terminal side in the right quadrant
go in either positive or negative direction based on original problem
if you have added or subtracted 360o or 2π, you need to go around multiple times.

4. What quadrant is it in (and sketch)?

5. What quadrant is it in? (radians)
Follow steps to make small positive angle
Put fraction in calculator (without the π)
If answer is < 0.5, it is in 1st quadrant
If answer is between 0.5 and 1, it is in 2nd quadrant
If answer is between 1 and 1.5, it is in 3rd quadrant
If answer is between 1.5 and 2, it is in 4th quadrant

6. Examples – which quadrant? (radians) (and sketch)

7. Complementary/Supplementary
Complementary angles add up to 90o (or π/2 for radians)
Supplementary angles add up to 180o (or π for radians)

8. Examples What angle is complementary/supplementary to 36o ?

9. Examples - radians What angle is complementary/supplementary to ?

10. Reference Angles
A reference angle is the acute angle that an angle makes with the x-axis

11. Finding Reference Angles
Follow steps to make small positive angle
Find out which quadrant it is in
In the 1st quadrant, the reference angle is the SAME as the angle itself
In the 2nd quadrant subtract the angle from 180o or π
In the 3rd quadrant subtract 180o or π from the angle
In the 4th quadrant subtract the angle from 360o or 2π

12. Examples Find the reference angle for the following angles. 37o 7π/4
-2π/3
-190o
17π/7
820o

13. Assessment 321 Write 3 new things you learned
Write 2 vocabulary words with their meaning
Write 1 thing you don’t understand