1. LESSON 6-1: ANGLES & THE UNIT CIRCLE BASIC GRAPHING OBJECTIVE: CONVERT BETWEEN DEGREE AND RADIAN MEASURE, PLACE ANGLES IN STANDARD POSITION & IDENTIFY CO-TERMINAL ANGLES, UNDERSTAND BASIC GRAPHS OF COSINE AND SINE.

2. VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y

3. VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y The ray drawn along the positive x-axis

4. VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y The ray drawn along the positive x-axis The ray from the origin that opens along the circle from the initial side

5. VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y The ray drawn along the positive x-axis The ray from the origin that opens along the circle from the initial side Any angle drawn from the origin with an initial side and terminal side

6. VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y The ray drawn along the positive x-axis The ray from the origin that opens along the circle from the initial side Any angle drawn from the origin with an initial side and terminal side Any two angle with the same terminal side, whether it open counter-clockwise or clockwise

7. VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y The ray drawn along the positive x-axis The ray from the origin that opens along the circle from the initial side Any angle drawn from the origin with an initial side and terminal side Any two angle with the same terminal side, whether it open counter-clockwise or clockwise The angle between the terminal side and the x-axis

8. VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y A circle drawn about the origin with radius = 1

9. VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y A circle drawn about the origin with radius = 1 The opening equivalent to one radius wrapped around circumference of the unit circle

10. VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y A circle drawn about the origin with radius = 1 The opening equivalent to one radius wrapped around circumference of the unit circle

11. VOCABULARY INITIAL SIDE: TERMINAL SIDE: STANDARD POSITION: CO-TERMINAL ANGLES: REFERENCE ANGLE: UNIT CIRCLE: RADIAN: x y

12. Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y 1 st draw where you think the angle ends

13. Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y Find the quadrants by remembering their placement

14. Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y x y Find the reference angle by remembering That it is always formed with x-axis

15. Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y Try this one

16. Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y Now this one Let’s check our work

17. Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y

18. Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y

19. Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y x y

20. Draw an angle with the given measure in standard position. Indicate which quadrant the terminal side falls in State the reference angle. x y x y

21. Checkpoint

22. COTERMINAL ANGLES

23. HOW DO I FIND COTERMINAL ANGLES? EXAMPLE: FIND ONE POSITIVE AND ONE NEGATIVE COTERMINAL ANGLE OF 315 O

24. RADIANS ↔ DEGREES CONVERTING BETWEEN DEGREES AND RADIANS: SET UP THE RATIO AND SOLVE FOR THE MISSING

25. RADIANS ↔ DEGREES Try converting these measures

26. RADIANS ↔ DEGREES

30. Here are some more to try

31. RADIANS ↔ DEGREES

32. Checkpoint