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The R-form rewrites a sin θ + b cos θ as a single sinusoid R sin(θ + α) or R cos(θ ± α). This topic covers finding R and α and using the form to solve equations and find maxima and minima. It's a key topic in A-Level and International A-Level (iAL) Pure Mathematics. This free interactive course teaches the method with worked examples and gives instant-feedback practice questions to lock it in.
How you do it
Expand R sin of theta plus alpha with the addition formula and compare coefficients. R is the square root of the sum of the squares, and tan alpha is one coefficient over the other. The maximum value is R and the minimum is minus R, which is what makes this form useful for modelling.
Before you start
Get the addition formulae straight before you begin. It underpins maximum and minimum values and modelling.
What you learn
Once it is one wave, its maximum and minimum are obvious — and equations you could not touch become easy. An expression like 3cosθ+4sinθ is a sum of two waves with the same period. The mark is usually for the θ at which it occurs — so always set the bracket equal to 0 or 180° and solve. The course works through why the R-form exists, maximum, minimum — and where, solving a cos θ + b sin θ = c, applications: modelling with the R-form and choosing and using the form. Every section has instant-feedback practice questions matched to Edexcel International A-Level and 9MA0 Pure, and the course finishes with full exam-style questions you mark yourself.
Related Topics
R sin(θ + α) Form is part of the Trigonometry strand of our free A-level maths courses, studied in the AS year. You work through 5 concepts and 5 worked examples, testing yourself at 5 points. Students often pair it with Radians, Arcs & Sectors, Reciprocal Trig Functions, Sine & Cosine Rules and Solving Trig Equations. Endless extra practice on this strand is available on the Trigonometry revision engine, which generates a fresh question each time.
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