Chapter 3: Further trigonometry Notes

Sections

1. 3A Three-dimensional trigonometry Mastered

   Solve 3D problems by breaking them into triangles: Pythagoras in three dimensions, the angle between a line and a plane, the angle between two planes, and problems needing a pronumeral across several triangles.

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2. 3B Compound-angle formulae Mastered

   The expansions of sin, cos and tan of α ± β, how they are proved from cos(α − β), and using them for exact values and simplifying expressions.

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3. 3C The double-angle formulae Mastered

   The formulae for sin 2θ, cos 2θ (three forms) and tan 2θ, the squared forms for cos²θ and sin²θ, exact values of half angles, and proving identities.

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4. 3D Trigonometric equations Mastered

   Solve trig equations using the compound and double-angle formulae: factoring, quadratics in one function, equations with different angles, homogeneous equations, and the danger of squaring.

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5. 3E The sum of sine and cosine Mastered

   Write a sin x + b cos x as R sin(x + α) or R cos(x − α) using an auxiliary angle, read off its maximum and minimum, and solve equations and inequations of the form a sin x + b cos x = c.

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