1. Unit 1, Lesson 1 Angles and their Measures

2. What is an angle? Two rays with the same Endpoint.

3. Make a table Term Definition Picture

4. Trigonometry vocabulary Initial side – start side of angle Terminal side – end side of angle Standard position – An angle whose initial side is on the positive x-axis Coterminal angle – Angles that have the same terminal side

5. Positive angles Initial side on the positive x-axis and rotate counterclockwise

6. Negative angles Initial side on the positive x-axis and rotate clockwise

7. Quadrants Quadrant III Quadrant I Quadrant II Quadrant IV

8. Angles of the axes

9. Variables you will see for angle measures

10. Examples What quadrant is the terminal side of the angle in? (Make a sketch of the angle)

11. Examples - Coterminal angles You can add or subtract multiples of 360 or -360 to find coterminal angles Find 2 coterminal angles (one positive and one negative) for 35 o Find 2 coterminal angles (one positive and one negative) for -23 o Find 2 coterminal angles (one positive and one negative) for 740 o

12. Decimal degree vs. degree/minute/second Sometimes angles are not whole numbers When this happens, they take 2 forms –Degree decimal - 76.5 o –Degree/minute/second (DMS) 53 o 18’ 23” To change from DMS to decimals, divide the minutes by 60 and the seconds by 3600 and add all together To change from decimal to DMS, multiply decimal by 60 – this is the minutes, then multiply resulting decimal by 3600, this is the seconds

13. Examples - DMS Convert to decimal 35 o 18’ 27” -142 o 54’ 32” Convert to DMS -23.873 o 740.5 o

14. Radians

15. Examples Change from degrees to radians Change from radians to degrees

16. Coterminal Examples using radians Add or subtract 2π to angle

17. Complementary/Supplementary Complementary angles add up to 90 o or Supplementary angles add up to 180 o or

18. Examples What angle is complementary to 36 o ? What angle is supplementary to 36 o ? What angle is complementary to ? What angle is supplementary to ?

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

20. 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 θ = central angle