1. θ

2. Trigonometric Ratios

3. θ Reference Angle Adjacent Leg Hypotenuse Opposite Leg Basic ratio definitions

4. + Counter clockwise - clockwise Initial Ray Terminal Ray Definition of an angle

5. Coterminal angles – angles with a common terminal ray Initial Ray Terminal Ray

6. Coterminal angles – angles with a common terminal ray Initial Ray Terminal Ray

7. Radian Measure

8. r r 1 Radian  57.3 o 360 o = 2 π radians 180 o = π radians Definition of Radians C= 2 πr C= 2 π radii C= 2 π radians

9. Converting Degrees ↔ Radians Recall Converts degrees to Radians Converts Radians to degrees more examples

10. Unit Circle – Radian Measure

12. Degrees

13. Circle Trigonometry Definitions (x, y) Radius = r Adjacent Leg = x Opposite Leg = y reciprocal functions

14. Unit - Circle Trigonometry Definitions (x, y) Radius = 1 Adjacent Leg = x Opposite Leg = y 1

15. Unit Circle – Trig Ratiossincostan (+, +) (-, -) (-, +) (+, -) Reference Angles Skip π/4’s

16. Unit Circle – Trig Ratiossincostan (+, +) (-, -) (-, +) (+, -)

17. Unit Circle – Trig Ratiossincostan (+, +) (-, -) (-, +) (+, -) sincostan 1 1 0 0 0 0 0 0 Ø Ø (0, -1) (0, 1) (1, 0)(-1, 0) 0 /2 π Quadrant Angles View π/4’s

18. Unit Circle – Radian Measuresincostan (+, +) (-, -) (-, +) (+, -) Degrees 1 sincostan 1 1 0 0 0 0 0 0 Ø Ø 0 /2 π Quadrant Angles

19. A unit circle is a circle with a radius of 1 unit. For every point P(x, y) on the unit circle, the value of r is 1. Therefore, for an angle θ in the standard position:

20. Special Right TrianglesThe Pythagoreans Graphs Rene’ DesCartes Trigonometry Hipparchus, Menelaus, Ptolemy

21. Reference Angle Calculation 2 nd Quadrant Angles3 rd Quadrant Angles4 th Quadrant Angles Return

22. Unit Circle – Degree Measure 0/360 150 240 300 315 330 180 210 225 270 30 90 120 135 45 60 Return

23. Unit Circle – Degree Measure 0/360 150 240 300 315 330 180 210 225 270 30 90 120 135 45 60 sincostan (+, +) (-, -) (-, +) (+, -) 30 45 60 Return 1 sincostan 1 1 0 0 0 0 0 0 Ø Ø 0/360 90 180 270 Quadrant Angles

24. Ex. # 6Ex. # 5 Ex. # 4Ex. # 3 return

25. Circle Trigonometry Definitions – Reciprocal Functions (x, y) Radius = r Adjacent Leg = x Opposite Leg = y return

26. Unit Circle – Radian Measure 1