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A LevelMaths: Pure 3CIERevision Notes3. Trigonometry3.2 Compound & Double Angle Formulae3.2.1 Compound Angle Formulae

Compound Angle Formulae (CIE A Level Maths: Pure 3)

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Roger

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Compound Angle Formulae

What are the compound angle formulae?

  • There are six compound angle formulae (also known as addition formulae), two each for sin, cos and tan:
  • For sin the +/- sign on the left-hand side matches the one on the right-hand side
sin left parenthesis A plus B right parenthesis identical to sin A cos B plus cos A sin B

sin left parenthesis A minus B right parenthesis identical to sin A cos B minus cos A sin B

  • For cos the +/- sign on the left-hand side is opposite to the one on the right-hand side
cos left parenthesis A plus B right parenthesis identical to cos A cos B minus sin A sin B

cos left parenthesis A minus B right parenthesis identical to cos A cos B plus sin A sin B

  • For tan the +/- sign on the left-hand side matches the one in the numerator on the right-hand side, and is opposite to the one in the denominator
tan left parenthesis A plus B right parenthesis identical to fraction numerator tan A plus tan B over denominator 1 minus tan A tan B end fraction

tan left parenthesis A minus B right parenthesis identical to fraction numerator tan A minus tan B over denominator 1 plus tan A tan B end fraction
  • You can derive the tan identity by:
    • Writing tan left parenthesis A plus B right parenthesis identical to fraction numerator sin left parenthesis A plus B right parenthesis over denominator cos left parenthesis A plus B right parenthesis end fraction
    • Dividing the numerator and denominator by cos A cos B

Examiner Tip

  • All these formulae are in the formulae booklet – you don't have to memorise them.

Worked example

Comp Angle Forms Example, A Level & AS Maths: Pure revision notes

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    Roger

    Author: Roger

    Expertise: Maths

    Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.