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Maths · Further Trigonometry

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Maths · AQA Paper 1

Further Trigonometry

Trigonometric Graphs and Exact Values (Higher tier)

Sketching and using the sine, cosine and tangent graphs, and solving equations between 0 and 360 degrees using exact values.

  • Sine The ratio of the opposite side to the hypotenuse.
  • Cosine The ratio of the adjacent side to the hypotenuse.
  • Tangent The ratio of the opposite side to the adjacent side.
The graphs of sine and cosine between 0 and 360 degrees, two waves between 1 and minus 1, with the cosine graph starting at its maximum.

The Sine Rule (Higher tier)

Using the sine rule to find sides and angles in triangles without a right angle.

  • Sine rule A rule linking sides and the sines of the opposite angles in any triangle.
  • Matching pair A side and the angle opposite to it.
  • Opposite Across the triangle, not touching.
A triangle with angles A, B and C and the sides a, b and c, where each side is opposite the angle with the same letter.

The Cosine Rule (Higher tier)

Using the cosine rule to find a side from two sides and the included angle, or an angle from three sides.

  • Cosine rule A rule linking three sides and one angle in any triangle.
  • Included angle The angle between two given sides.
  • Hypotenuse The longest side of a right-angled triangle.
A triangle with the angle A between the sides b and c, and the side a opposite to angle A.

Area of a Triangle and Segments (Higher tier)

Using half ab sin C to find areas, sides and angles, and finding the area of a segment of a circle.

  • Area The amount of surface inside a shape.
  • Included angle The angle between two given sides.
  • Segment The part of a circle cut off by a chord.
A triangle with the sides a and b and the angle C between them, with the perpendicular height h shown as a dashed line.

Trigonometry in 3D and Mixed Problems (Higher tier)

Finding lengths and angles in cuboids and pyramids, and combining Pythagoras and the sine and cosine rules.

  • Space diagonal A line from one corner of a cuboid to the opposite corner.
  • Plane A flat surface.
  • Apex The top point of a pyramid.
A cuboid ABCDEFGH with the base diagonal AC, the space diagonal AG and the angle theta between them.