2. DEdwards Square on Hypotenuse Square on Leg 1 Square on Leg 2 = +

3.  Sine  Cosine  Tangent

4. Prove: . .

5. Special Angles θ 0°0° 30 ° 45 ° 60 ° 90 ° Sin θ Cos θ Tan θ ?? ? ? ? ? ? ? ? ? ? ? ? ? ? DEdwards proof

6.  Sin 30 ° =  Cos 30 ° =  Tan 30 ° =  Sin 60 ° =  Cos 60 ° =  Tan 60 ° = 2 2 2 60 ° 1 30 ° table

7.  Sin 45 ° =  Cos 45 ° =  Tan 45 ° = 1 1 45 ° table

8. Trigonometric Graphs are PERIODIC i.e. they repeat themselves after a “cycle” is complete

9. y-intercept = 0 x-intercepts = 0 °, ±180 °, ±360 °

10. y-intercept = 1 x-intercepts = ±90 °, ±270 °

12.  Complementary Relationships  Sin x = Cos ( 90 - x)  Cos x = Sin ( 90 - x)  Tan x =

13.  Supplementary Relationships  Sin x = Sin ( 180 - x)  Cos x = - Cos ( 180 - x)  Tan x = - Tan ( 180 - x)

14. The function has ASYMPTOTES at these points

15. (0,1) THE UNIT CIRCLE Circle on the Cartesian plane with radius of 1 unit

16. (0,1) THE UNIT CIRCLE

17. (0,1) THE UNIT CIRCLE: 1 st Quadrant Theta θ : Angle between Terminal side & Initial side Reference Angle α : Acute Angle between Terminal Side & x-axis

18. (0,1) THE UNIT CIRCLE: 2 nd Quadrant Theta, θ Reference Angle α

19. (0,1) THE UNIT CIRCLE: 3 rd Quadrant Theta, θ Reference Angle α

20. (0,1) THE UNIT CIRCLE: 4 th Quadrant Theta, θ Reference Angle α

21. (0,1) THE UNIT CIRCLE Coordinates of points on the unit circle show (cos θ, sin θ) When the terminal side is drawn through that point

22. (0,1) THE UNIT CIRCLE (cos θ, sin θ) x P(a, b) θ ° O X

23. (0,1) THE UNIT CIRCLE Coordinates of points on the unit circle show (cos θ, sin θ) When the terminal side is drawn through that point x θ=90 ° cos90 °=0 sin90 ° =1 Hence point on circle is (0,1)

24. (0,1) THE UNIT CIRCLE Coordinates of points on the unit circle show (cos θ, sin θ) When the terminal side is drawn through that point x θ=180 ° Cos180° = -1 Sin 180° = 0 Hence point on circle is (-1,0)

25. (0,1) THE UNIT CIRCLE Coordinates of points on the unit circle show (cos θ, sin θ) When the terminal side is drawn through that point x θ=270 ° Cos 270° = 0 Sin 270° = -1 Hence point on circle is (0, -1) DEdwards

26. (0,1) THE UNIT CIRCLE (cos θ, sin θ) x θ=30 ° Cos 30 °= 0.866=0.9 (1dp) sin30 ° = 0.5 Hence point on circle is (0.9, 0.5) (0.9, 0.5) θ=30 °

27. (0,1) THE 1 st QUADRANT 0 <θ ≤ 90 For all points (x,y) x is positive & y is positive So, all points (cos θ,sin θ ) Cos θ :positive Sin θ : positive Tan θ = sin θ /cos θ=positive ll are Positive

28. (0,1) THE 2 nd QUADRANT 90 ° <θ ≤ 180° For all points (x,y) x is negative & y is positive So, all points (cos θ,sin θ ) Cos θ :negative Sin θ : positive Tan θ = sin θ /cos θ=negative ll are Positive INE (only) is Positive

29. (0,1) THE 3 rd QUADRANT 180 ° <θ ≤ 270° For all points (x,y) x is negative & y is negative So, all points (cos θ,sin θ ) Cos θ :negative Sin θ : negative Tan θ = sin θ /cos θ=positive ll are Positive INE (only) is Positive AN (only) is Positive

30. (0,1) THE 4 th QUADRANT 270 ° <θ ≤ 360° For all points (x,y) x is positive & y is negative So, all points (cos θ,sin θ ) Cos θ :positive Sin θ : negative Tan θ = sin θ /cos θ=negative ll are Positive INE (only) is Positive AN (only) is Positive OS (only) is Positive

31. (0,1) ll are Positive INE (only) is Positive AN (only) is Positive OS (only) is Positive

32.  “CAST” Relationships  Sin x = Sin (180 - x) = -Sin (180 + x) = Sin ( 360 - x)  Cos x = -Cos (180 - x) = -Cos (180+ x) = Cos (360 - x)  Tan x = -Tan (180 - x) = Tan (180+ x) = -Tan(360 - x)