PROGRAMME F8 TRIGONOMETRY.

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Presentation transcript:

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 Reciprocal ratios Pythagoras’ theorem Special triangles

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

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

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

Programme F8: Trigonometry Angles Trigonometric ratios

Programme F8: Trigonometry Angles Trigonometric ratios

Programme F8: Trigonometry Angles Reciprocal ratios

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

Programme F8: Trigonometry Angles Special triangles Right-angled isosceles

Programme F8: Trigonometry Angles Special triangles Half equilateral

Programme F8: Trigonometry Angles Special triangles Half equilateral

Programme F8: Trigonometry Angles Trigonometric identities Trigonometric formulas

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

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

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

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

Programme F8: Trigonometry Angles Trigonometric identities Trigonometric formulas

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

Programme F8: Trigonometry Trigonometric formulas Sums and differences of angles

Programme F8: Trigonometry Trigonometric formulas Double angles

Programme F8: Trigonometry Trigonometric formulas Sums and differences of ratios

Programme F8: Trigonometry Trigonometric formulas Products of ratios

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