Maths · AQA Paper 1
Further Trigonometry
The further trigonometry skills tested on AQA Paper 1: trigonometric graphs and exact values, the sine rule, the cosine rule, the area of a triangle, and trigonometry in three dimensions, all done without a calculator.
Lessons
Ticks are remembered on this device only.
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1
Trigonometric Graphs and Exact Values
Sketching and using the sine, cosine and tangent graphs, and solving equations between 0 and 360 degrees using exact values.
9 terms -
2
The Sine Rule
Using the sine rule to find sides and angles in triangles without a right angle.
9 terms -
3
The Cosine Rule
Using the cosine rule to find a side from two sides and the included angle, or an angle from three sides.
9 terms -
4
Area of a Triangle and Segments
Using half ab sin C to find areas, sides and angles, and finding the area of a segment of a circle.
9 terms -
5
Trigonometry in 3D and Mixed Problems
Finding lengths and angles in cuboids and pyramids, and combining Pythagoras and the sine and cosine rules.
9 terms
Key terms in this chapter
All 45, gathered from every lesson.
- 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.
- Period
- The distance after which a graph repeats.
- Asymptote
- A line that a graph approaches but never touches.
- Amplitude
- Half the distance between the maximum and minimum values.
- Exact value
- A value written with fractions and surds, not as a decimal.
- Symmetry
- A balance in a graph, so that values are repeated.
- Periodic
- Repeating at regular intervals.
- 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.
- Exact value
- A value written with fractions and surds.
- Acute angle
- An angle less than \(90^\circ\).
- Obtuse angle
- An angle between \(90^\circ\) and \(180^\circ\).
- Surd
- A root that cannot be written as a whole number or fraction.
- Subject
- The letter on its own on one side of a formula.
- Ratio
- A comparison of two quantities.
- 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.
- Obtuse angle
- An angle between \(90^\circ\) and \(180^\circ\).
- Acute angle
- An angle less than \(90^\circ\).
- Exact value
- A value written with fractions and surds.
- Subject
- The letter on its own on one side of a formula.
- Square root
- The number that multiplies by itself to give another.
- Substitute
- Replace letters with numbers.
- 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.
- Sector
- The part of a circle between two radii.
- Exact value
- A value written with fractions, surds and \(\pi\).
- Chord
- A straight line joining two points on a circle.
- Perpendicular height
- The shortest distance from a vertex to the opposite side.
- Surd
- A root that cannot be written as a whole number or fraction.
- Radius
- The distance from the centre of a circle to its edge.
- 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.
- Cuboid
- A solid with six rectangular faces.
- Pyramid
- A solid with a flat base and sloping triangular faces meeting at the apex.
- Hypotenuse
- The longest side of a right-angled triangle.
- Exact value
- A value written with surds, not as a decimal.
- Angle between a line and a plane
- The angle between the line and its shadow on the plane.
- Perpendicular
- At \(90^\circ\).