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# Special angles

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How to find the values of "special" angles in Trigonometry

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• ### Special angles

1. 1. Exact Values of the Trig Ratios Thursday 26th May 2011
2. 2. Construct an right angled isosceles triangle
3. 3. 45° 45°Construct an right angled isosceles triangle
4. 4. 1 1Make the sides the simplest they can be....
5. 5. 45° 1 45° 1Make the sides the simplest they can be....
6. 6. 45° 1 45° 1Find the hypotenuse....
7. 7. 45° 2 1 45° 1Find the hypotenuse....
8. 8. o 1 tan 45 = = 1 1 45° o 1 2 sin 45 = = 2 2 1 o 1 2 cos 45 = = 2 2 45° 1deﬁne the Trig ratios....
9. 9. o 1 tan 45 = = 1 1 45° o 1 2 2 sin 45 = 2 = 2 1 o 1 2 cos 45 = = 2 2 45° 1deﬁne the Trig ratios....
10. 10. o 1 tan 45 = = 1 1 45° 1 45° 1remember the process not the values :)
11. 11. o 1 tan 45 = = 1 1 45° 2 1 45° 1remember the process not the values :)
12. 12. o 1 tan 45 = = 1 1 45° o 1 2 2 sin 45 = 2 = 2 1 45° 1remember the process not the values :)
13. 13. o 1 tan 45 = = 1 1 45° o 1 2 2 sin 45 = 2 = 2 1 o 1 2 cos 45 = = 2 2 45° 1remember the process not the values :)
14. 14. Construct an equilateral triangle...
15. 15. Construct an equilateral triangle...
16. 16. 60° 60° 60°Construct an equilateral triangle...
17. 17. 60°60° 60° with simple side lengths
18. 18. 60°2 260° 60° 2 with simple side lengths
19. 19. 60° 2 260° 60° 2 bisect the top angle
20. 20. 30° 2 260° 60° 1 1 bisect the top angle
21. 21. 30° 2 260° 60° 1 1 ﬁnd the perpendicular height
22. 22. 30° 2 2 360° 60° 1 1 ﬁnd the perpendicular height
23. 23. 30° 2 2 60° 60° 1 1Read off the trig ratios in the constructed right angled triangle
24. 24. 30° 2 2 360° 60° 1 1
25. 25. 30° 2 2 3 60° 60° o 3 1 1sin 60 = 2
26. 26. 30° 2 2 3 60° 60° o 3 1 1sin 60 = 2 o 1cos 60 = 2
27. 27. 30° 2 2 3 60° 60° o 3 1 1sin 60 = 2 o 1cos 60 = 2 o 3tan 60 = = 3 1
28. 28. 30° 2 2 3 60° 60° o 3 1 1 o 1sin 60 = sin 30 = 2 2 o 1cos 60 = 2 o 3tan 60 = = 3 1
29. 29. 30° 2 2 3 60° 60° o 3 1 1 o 1sin 60 = sin 30 = 2 2 o 1 o 3cos 60 = cos 30 = 2 2 o 3tan 60 = = 3 1
30. 30. 30° 2 2 3 60° 60° o 3 1 1 o 1sin 60 = sin 30 = 2 2 o 1 o 3cos 60 = cos 30 = 2 2 o 3 1 3tan 60 = = 3 o tan 30 = = 1 3 3
31. 31. Remember the process not the results! :) o 1tan 45 = = 1 3 o 1 1 o sin 60 = sin 30 = 2 2 o 1 2 o 1 o 3sin 45 = = cos 60 = cos 30 = 2 2 2 2 o 1 2 o 3 o 1 3cos 45 = = tan 60 = = 3 tan 30 = = 2 2 1 3 3