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

2. Angles and their Measures - Radians Essential question – How is a radian related to a degree?

3. Radians Angle degrees can also be expressed in radians Radians is the ratio of the length of an arc to its radius Radians are expressed in terms of = 180 o To change from degrees to radians, multiply by and reduce. To change from radians to degrees, multiply by

4. Examples Change from degrees to radians Change from radians to degrees

5. Coterminal using radians Add or subtract 2π to angle

6. Examples Find a positive and negative coterminal angle

7. What quadrant is it in? If angle is negative, find positive coterminal angle Put fraction in calculator (without the π) If answer is < 0.5, it is in 1 st quadrant If answer is between 0.5 and 1, it is in 2 nd quadrant If answer is between 1 and 1.5, it is in 3 rd quadrant If answer is between 1.5 and 2, it is in 4 th quadrant

8. Examples – which quadrant? Find a positive and negative coterminal angle

9. Complementary/Supplementary Complementary angles add to Supplementary angles add to

10. Examples What angle is complementary/supplementary to ?

11. Finding arc lengths S=rθ S is arc length r = radius θ = central angle, must be in radians

12. Examples Find the length of the arc with radius 20 in and central angle of π/4 Find the length of an arc with radius 5 m and central angle of 180 o Find the measure of the central angle is arc length is 6 in and radius is 18 in

13. Reference Angles

14. A reference angle is the acute angle that an angle makes with the x-axis

15. Finding Reference Angles If the angle is negative, you must make it positive by adding 360 or 2 π If the angle is more than 360 or 2 π, you must subtract 360 or 2 π until it is less Now you can find the reference angle In the 1 st quadrant, the reference angle is the SAME as the angle itself In the 2 nd quadrant subtract the angle from 180 o or π In the 3 rd quadrant subtract 180 o or π from the angle In the 4 th quadrant subtract the angle from 360 o or 2π

16. Examples Find the reference angle for the following angles. 37 o 7π/4 -2π/3 -190 o 17π/7 810 o

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