Compound and double angles, R form and identities
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The teaching part (1 min) is free to watch. A free account opens the whole lecture: 5 practice questions, 2 real past-paper questions with the answers explained, the mistakes that lose marks, the full-marks tip, a one-card summary and a quick quiz.
What this lecture covers
- One wave from two
- Compound angle formulae
- Double angle formulae
Read the transcript of the teaching part
Last time
Before we start: last time, in Exponential inequalities, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.
One wave from two
A sound made of a sine wave and a cosine wave of the same frequency is still a single smooth wave. The R form shows exactly which wave. Together with the compound and double angle formulae, it solves almost every trigonometry equation in Paper 3.
Compound angle formulae
Sine of A plus B is sine A cosine B, plus cosine A sine B. For minus, change the middle sign. Cosine of A plus B is cosine A cosine B, minus sine A sine B. The sign flips. Tangent of A plus B is tan A plus tan B, over one minus tan A tan B.
Double angle formulae
Sine two A is two sine A cosine A. Cosine two A has three forms: cosine squared minus sine squared, or two cosine squared minus one, or one minus two sine squared. Tangent two A is two tan A over one minus tan squared A. Choose the cosine form that leaves one trig function, matching the other terms in the equation.
How often it comes up
How often Cambridge has asked each part, counted by ExamYard from every past paper in its question bank: Compound angle equations · Double angle equations · Expressing in R form · Proving and using identities.
The whole chapter: Trigonometry.
Chapter 3.3: Trigonometry
- Compound and double angles, R form and identities 6 min
Also for A Level Maths 9709 Paper 3
Which topics come up most in A Level Maths 9709 Paper 3 past papers, counted from every paper since 2004.