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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

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


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