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PROGRAMME F8

PROGRAMME F8. TRIGONOMETRY. Programme F8: Trigonometry. Angles Trigonometric identities Trigonometric formulas. Programme F8: Trigonometry. Angles Trigonometric identities Trigonometric formulas. Programme F8: Trigonometry. Angles Rotation Radians Triangles Trigonometric ratios

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PROGRAMME F8

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  1. PROGRAMME F8 TRIGONOMETRY

  2. Programme F8: Trigonometry Angles Trigonometric identities Trigonometric formulas

  3. Programme F8: Trigonometry Angles Trigonometric identities Trigonometric formulas

  4. Programme F8: Trigonometry Angles Rotation Radians Triangles Trigonometric ratios Reciprocal ratios Pythagoras’ theorem Special triangles

  5. Programme F8: Trigonometry Angles Rotation When a straight line is rotated about a point it sweeps out an angle that can be measured in degrees or radians A straight line rotating through a full angle and returning to its starting point is said to have rotated through 360 degrees – 360o One degree = 60 minutes and one minute = 60 seconds

  6. Programme F8: Trigonometry Angles Radians When a straight line of length r is rotated about one end so that the other end describes an arc of length r the line is said to have rotated through 1 radian – 1 rad

  7. Programme F8: Trigonometry Angles Triangles All triangles possess shape and size. The shape of a triangle is governed by the three angles and the size by the lengths of the three sides

  8. Programme F8: Trigonometry Angles Trigonometric ratios

  9. Programme F8: Trigonometry Angles Trigonometric ratios

  10. Programme F8: Trigonometry Angles Reciprocal ratios

  11. Programme F8: Trigonometry Angles Pythagoras’ theorem The square on the hypotenuse of a right-angled triangle is equal to the sum of the squares on the other two sides

  12. Programme F8: Trigonometry Angles Special triangles Right-angled isosceles

  13. Programme F8: Trigonometry Angles Special triangles Half equilateral

  14. Programme F8: Trigonometry Angles Special triangles Half equilateral

  15. Programme F8: Trigonometry Angles Trigonometric identities Trigonometric formulas

  16. Programme F8: Trigonometry Trigonometric identities The fundamental identity Two more identities Identities for compound angles

  17. Programme F8: Trigonometry Trigonometric identities The fundamental identity The fundamental trigonometric identity is derived from Pythagoras’ theorem

  18. Programme F8: Trigonometry Trigonometric identities Two more identities Dividing the fundamental identity by cos2

  19. Programme F8: Trigonometry Trigonometric identities Two more identities Dividing the fundamental identity by sin2

  20. Programme F8: Trigonometry Angles Trigonometric identities Trigonometric formulas

  21. Programme F8: Trigonometry Trigonometric formulas Sums and differences of angles Double angles Sums and differences of ratios Products of ratios

  22. Programme F8: Trigonometry Trigonometric formulas Sums and differences of angles

  23. Programme F8: Trigonometry Trigonometric formulas Double angles

  24. Programme F8: Trigonometry Trigonometric formulas Sums and differences of ratios

  25. Programme F8: Trigonometry Trigonometric formulas Products of ratios

  26. Programme F8: Trigonometry Learning outcomes • Convert angles measured in degrees, minutes and seconds into decimal degrees • Convert degrees into radians and vice versa • Use a calculator to determine the values of trigonometric ratios for any acute angle • Verify trigonometric identities

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