Trigonometry progresses from right-angled triangle ratios (SOH CAH TOA) to the sine and cosine rules for any triangle. Extended students also cover trig graphs, equations, and 3D problems.
In a right-angled triangle: sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent. Finding sides: rearrange formula. Finding angles: use inverse trig (sin⁻¹, cos⁻¹, tan⁻¹). Pythagoras\'s theorem: a² + b² = c². These apply ONLY to right-angled triangles.
For ANY triangle. Sine rule: a/sinA = b/sinB = c/sinC (use with AAS, ASA, or the ambiguous SSA case). Cosine rule: a² = b² + c² − 2bc·cosA (use with SAS or SSS). Area of triangle = ½ab·sinC. Choose the rule based on what information is given.
Three-digit angles measured clockwise from North: 000° to 360°. Back-bearing = bearing ± 180°. Combine with trigonometry to solve navigation problems. Common exam question: two boats/planes with bearings and distances — find the distance between them or the bearing from one to the other.
Graphs of sin x, cos x, tan x for 0° ≤ x ≤ 360°. Properties: amplitude, period, symmetry. Solving trig equations graphically and algebraically (finding all solutions in a range). 3D trigonometry: identifying right-angled triangles within 3D shapes (cuboids, pyramids) and applying trig to find angles and distances.
Sine rule: when you know a side and its opposite angle plus one more piece (AAS or ASA). Cosine rule: when you know two sides and the included angle (SAS) or all three sides (SSS). If in doubt: if you have a matched pair (side + opposite angle), start with sine rule. If not, use cosine rule. The area formula ½ab sinC works when you know two sides and the included angle.
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