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Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
Special angles
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Special angles

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

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

Published in: Education
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  • Transcript

    • 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 1Make the sides the simplest they can be....
    • 5. 45° 1 45° 1Make the sides the simplest they can be....
    • 6. 45° 1 45° 1Find the hypotenuse....
    • 7. 45° 2 1 45° 1Find 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° 1define 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° 1define the Trig ratios....
    • 10. o 1 tan 45 = = 1 1 45° 1 45° 1remember the process not the values :)
    • 11. o 1 tan 45 = = 1 1 45° 2 1 45° 1remember the process not the values :)
    • 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. 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. 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°2 260° 60° 2 with simple side lengths
    • 19. 60° 2 260° 60° 2 bisect the top angle
    • 20. 30° 2 260° 60° 1 1 bisect the top angle
    • 21. 30° 2 260° 60° 1 1 find the perpendicular height
    • 22. 30° 2 2 360° 60° 1 1 find the perpendicular height
    • 23. 30° 2 2 60° 60° 1 1Read off the trig ratios in the constructed right angled triangle
    • 24. 30° 2 2 360° 60° 1 1
    • 25. 30° 2 2 3 60° 60° o 3 1 1sin 60 = 2
    • 26. 30° 2 2 3 60° 60° o 3 1 1sin 60 = 2 o 1cos 60 = 2
    • 27. 30° 2 2 3 60° 60° o 3 1 1sin 60 = 2 o 1cos 60 = 2 o 3tan 60 = = 3 1
    • 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. 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° 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. 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

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