Trigonometry
Build and connect the representations and methods in trigonometry.
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Before you begin
Build and connect the representations and methods in trigonometry.
Learning goals
- Use and justify Pythagoras’ theorem
- Use trigonometric ratios in right-angled triangles
- Use sine and cosine rules for general triangles
Syllabus statements covered
- use of Pythagoras’ theorem • determining whether a triangle is right-angled given the lengths of three sides • use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles • extending sine and cosine to obtuse angles • use of the formula ½ab sin C for the area of a triangle • use of sine rule and cosine rule for any triangle • problems in two and three dimensions including those involving angles of elevation and depression and bearings Sine/cosine rules and two-/three-dimensional problems (including elevation, depression and bearings) are tested only in Paper 2 Section B.
- use of Pythagoras’ theorem
- determining whether a triangle is right-angled given the lengths of three sides.
- use of trigonometric ratios (sine, cosine and tangent) of acute angles to calculate unknown sides and angles in right-angled triangles
- extending sine and cosine to obtuse angles
- use of the formula ½ab sin C for the area of a triangle
- use of sine rule and cosine rule for any triangle
- problems in two and three dimensions including those involving angles of elevation and depression and bearings
Lessons
Work through them in order.
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- Pythagoras and its converseG2 Mathematics 2027 · Normal (Academic) Secondary 2 Mathematics 2021Use the side opposite a right angle and test whether three lengths form a right triangle.
- Right-triangle sine, cosine and tangentG2 Mathematics 2027 · Normal (Academic) Secondary 3–4 Mathematics 2022Name sides relative to the chosen acute angle and choose a ratio using the available quantities.
- Sine rule, cosine rule and triangle areaG2 Mathematics 2027 · Normal (Academic) Secondary 3–4 Mathematics 2022Choose a rule from the given sides and included angles, and check ambiguous sine-rule solutions.
- Bearings and three-dimensional trianglesG2 Mathematics 2027 · Normal (Academic) Secondary 3–4 Mathematics 2022Draw the relevant plane triangle and keep horizontal projections distinct from sloping lengths.
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