Trigonometry

Radians, three new functions, and a toolkit of identities that turns hard equations into easy ones — DfE content area E. This builds directly on the Year 1 work on trig graphs, identities and equations.

• An Overview — radians, the full set of identities, how to choose the right tool, and the common mistakes

The content statements

• Radians, Arcs and Sectors — radian measure, exact values, arc length, sector and segment areas
• Small Angle Approximations — sin θ ≈ θ, cos θ ≈ 1 − θ²/2, tan θ ≈ θ, and using them
• Reciprocal and Inverse Functions — sec, cosec and cot; arcsin, arccos and arctan; the Pythagorean identities
• Compound and Double Angles — the addition formulae, double angle formulae, exact values and equations
• The R cos(x + a) Form — writing a cos θ + b sin θ as a single wave, maxima, minima and equations
• Trigonometric Proof and Modelling — proving identities, solving equations in radians, and modelling tides, wheels and daylight

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Each page has step-by-step notes, several worked examples, a quick-reference grid and ten practice questions with fully worked solutions.