1. All Six Trigonometric Functions
Finding
All Six Trigonometric Functions of
The Quadrantals

3. Let us now decrease the value of y and keep the x-value equal to 1
Let is consider an angle in the First Quadrant whose terminal side passes through a point (1, y)
Let us now decrease the value of y and keep the x-value equal to 1

4. Let is consider an angle in the First Quadrant whose terminal side passes through a point (1, y)
Let us now decrease the value of y again and keep the x-value equal to 1

5. Let is consider an angle in the First Quadrant whose terminal side passes through a point (1, y)
Let us now decrease the value of y again and keep the x-value equal to 1

6. Let is consider an angle in the First Quadrant whose terminal side passes through a point (1, y)
Let us now decrease the value of y again and keep the x-value equal to 1

7. The Terminal side passes through the point (1, 0)
And When
Getting closer and closer to ?

8. Using a Calculator we could complete the table below
The Terminal side passes through the point (1, 0)
And When
Using a Calculator we could complete the table below

9. We see the Cosine is getting closer and closer to 1
And the Sine is getting closer and closer to 0

10. Now we can use these observations to find all Six Trig Functions

11. What about the Tangent?
Remember

12. Reciprocals

13. Therefore the Reciprocal is
Reciprocals
Therefore the Reciprocal is

14. All Six Trigonometric Functionsof

15. If we made an ordered pair (cosine, sine) It would be (1,0) which were the coordinates of the point that the terminal side passes through when

16. 180

17. Let us now decrease the value of y and keep the x-value equal to –1
Let is consider an angle in the Second Quadrant whose terminal side passes through a point (–1, y)
Let us now decrease the value of y and keep the x-value equal to –1

18. Let us now decrease the value of y again and keep the x-value equal to –1

19. The Terminal side passes through the point (–1, 0)
And When
Getting closer and closer to ?

20. Using a Calculator we could complete the table below
The Terminal side passes through the point (–1, 0)
And When
Using a Calculator we could complete the table below

21. We see the Cosine is getting closer and closer to –1
And the Sine is getting closer and closer to 0

22. Now we can use these observations to find all Six Trig Functions

23. What about the Tangent?
Remember

24. Reciprocals

25. All Six Trigonometric Functionsof

26. If we made an ordered pair (cosine, sine) It would be (–1,0) which were the coordinates of the point that the terminal side passes through when

27. 90

28. Let us now decrease the value of x and keep the y-value equal to 1
Let is consider an angle in the First Quadrant whose terminal side passes through a point (x, 1)
Let us now decrease the value of x and keep the y-value equal to 1

29. Let is consider an angle in the First Quadrant whose terminal side passes through a point (x, 1)
Let us now decrease the value of x again and keep the y-value equal to 1

30. Let is consider an angle in the First Quadrant whose terminal side passes through a point (x, 1)
Let us now decrease the value of x again and keep the y-value equal to 1

31. The Terminal side passes through the point (0, 1)
And When
Getting closer and closer to ?

32. Using a Calculator we could complete the table below
The Terminal side passes through the point (0, 1)
And When
Using a Calculator we could complete the table below

33. We see the Cosine is getting closer and closer to 0
And the Sine is getting closer and closer to 1

34. Now we can use these observations to find all Six Trig Functions

35. What about the Tangent?
Remember

36. Reciprocals

37. All Six Trigonometric Functionsof

38. If we made an ordered pair (cosine, sine) It would be (0,1) which were the coordinates of the point that the terminal side passes through when

39. 270

40. Let us now decrease the value of x and keep the y-value equal to –1
Let is consider an angle in the Fourth Quadrant whose terminal side passes through a point (x, –1)
Let us now decrease the value of x and keep the y-value equal to –1

41. Let is consider an angle in the Fourth Quadrant whose terminal side passes through a point (x, –1)
Let us now decrease the value of x again and keep the y-value equal to –1

42. The Terminal side passes through the point (0,–1)
And When
Getting closer and closer to ?

43. Using a Calculator we could complete the table below
The Terminal side passes through the point (0,–1)
And When
Using a Calculator we could complete the table below

44. We see the Cosine is getting closer and closer to 0
And the Sine is getting closer and closer to –1

45. Now we can use these observations to find all Six Trig Functions

46. What about the Tangent?
Remember

47. Reciprocals

48. All Six Trigonometric Functionsof

49. If we made an ordered pair (cosine, sine) It would be (0,–1 ) which were the coordinates of the point that the terminal side passes through when

50. The Coterminal Angle Definition
What About
360
Remember
The Coterminal Angle Definition

51. Definition
If is the degree measure of an angle, then all angles coterminal with this angle have degree measure
where k is an integer.

52. What About
Same As

53. Summary
Summary

54. If we made an ordered pair (cosine, sine) It would be (1,0) which were the coordinates of the point that the terminal side passes through when

55. If we made an ordered pair (cosine, sine) It would be (–1,0) which were the coordinates of the point that the terminal side passes through when

56. If we made an ordered pair (cosine, sine) It would be (0,1) which were the coordinates of the point that the terminal side passes through when

57. If we made an ordered pair (cosine, sine) It would be (0,–1 ) which were the coordinates of the point that the terminal side passes through when