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STROUD Worked examples and exercises are in the text Programme F9: Trigonometry PROGRAMME F9 TRIGONOMETRY.

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Presentation on theme: "STROUD Worked examples and exercises are in the text Programme F9: Trigonometry PROGRAMME F9 TRIGONOMETRY."— Presentation transcript:

1 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry PROGRAMME F9 TRIGONOMETRY

2 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Angles Trigonometric identities Trigonometric formulas

3 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Angles Trigonometric identities Trigonometric formulas

4 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Angles Rotation Radians Triangles Trigonometric ratios Reciprocal ratios Pythagoras ’ theorem Special triangles

5 STROUD Worked examples and exercises are in the text Programme F9: 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 – 360° One degree = 60 minutes and one minute = 60 seconds

6 STROUD Worked examples and exercises are in the text Programme F9: 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 STROUD Worked examples and exercises are in the text Programme F9: 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 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Angles Trigonometric ratios

9 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Angles Trigonometric ratios

10 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Angles Reciprocal ratios

11 STROUD Worked examples and exercises are in the text Programme F9: 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 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Angles Special triangles Right-angled isosceles

13 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Angles Special triangles Half equilateral

14 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Angles Special triangles Half equilateral

15 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Angles Trigonometric identities Trigonometric formulas

16 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Angles Trigonometric identities Trigonometric formulas

17 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Trigonometric identities The fundamental identity Two more identities Identities for compound angles

18 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Trigonometric identities The fundamental identity The fundamental trigonometric identity is derived from Pythagoras ’ theorem

19 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Trigonometric identities Two more identities Dividing the fundamental identity by

20 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Trigonometric identities Two more identities Dividing the fundamental identity by

21 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Angles Trigonometric identities Trigonometric formulas

22 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Angles Trigonometric identities Trigonometric formulas

23 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Trigonometric formulas Sums and differences of angles Double angles Sums and differences of ratios Products of ratios

24 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Trigonometric formulas Sums and differences of angles

25 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Trigonometric formulas Double angles

26 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Trigonometric formulas Sums and differences of ratios

27 STROUD Worked examples and exercises are in the text Programme F9: Trigonometry Trigonometric formulas Products of ratios

28 STROUD Worked examples and exercises are in the text Programme F9: 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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