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

1. Exact Values of the Trig Ratios
Thursday 26th May 2011

2. Construct an right angled isosceles triangle

3. 45°
45°
Construct an right angled isosceles triangle

4. 1
1
Make the sides the simplest they can be....

5. 45°
1
45°
1
Make the sides the simplest they can be....

6. 45°
1
45°
1
Find the hypotenuse....

7. 45°
2
1
45°
1
Find the hypotenuse....

8. o 1
tan 45 = = 1
1
45°
o 1 2
sin 45 = =
2 2
1
o 1 2
cos 45 = =
2 2
45°
1
define the Trig ratios....

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°
1
define the Trig ratios....

10. o 1
tan 45 = = 1
1
45°
1
45°
1
remember the process not the values :)

11. o 1
tan 45 = = 1
1
45°
2
1
45°
1
remember the process not the values :)

12. o 1
tan 45 = = 1
1
45°
o 1 2
2 sin 45 =
2
=
2
1
45°
1
remember the process not the values :)

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°
1
remember the process not the values :)

14. Construct an equilateral triangle...

15. Construct an equilateral triangle...

16. 60°
60° 60°
Construct an equilateral triangle...

17. 60°
60° 60°
with simple side lengths

18. 60°
2 2
60° 60°
2
with simple side lengths

19. 60°
2 2
60° 60°
2
bisect the top angle

20. 30°
2 2
60° 60°
1 1
bisect the top angle

21. 30°
2 2
60° 60°
1 1
find the perpendicular height

22. 30°
2 2
3
60° 60°
1 1
find the perpendicular height

23. 30°
2 2
60° 60°
1 1
Read off the trig ratios in the constructed right angled
triangle

24. 30°
2 2
3
60° 60°
1 1

25. 30°
2 2
3
60° 60°
o 3 1 1
sin 60 =
2

26. 30°
2 2
3
60° 60°
o 3 1 1
sin 60 =
2
o 1
cos 60 =
2

27. 30°
2 2
3
60° 60°
o 3 1 1
sin 60 =
2
o 1
cos 60 =
2
o 3
tan 60 = = 3
1

28. 30°
2 2
3
60° 60°
o 3 1 1 o 1
sin 60 = sin 30 =
2 2
o 1
cos 60 =
2
o 3
tan 60 = = 3
1

29. 30°
2 2
3
60° 60°
o 3 1 1 o 1
sin 60 = sin 30 =
2 2
o 1 o 3
cos 60 = cos 30 =
2 2
o 3
tan 60 = = 3
1

30. 30°
2 2
3
60° 60°
o 3 1 1 o 1
sin 60 = sin 30 =
2 2
o 1 o 3
cos 60 = cos 30 =
2 2
o 3 1 3
tan 60 = = 3 o
tan 30 = =
1 3 3

31. Remember the process not
the results! :)
o 1
tan 45 = = 1 3 o 1
1 o
sin 60 = sin 30 =
2 2
o 1 2 o 1 o 3
sin 45 = = cos 60 = cos 30 =
2 2 2 2
o 1 2 o 3 o 1 3
cos 45 = = tan 60 = = 3 tan 30 = =
2 2 1 3 3