AQA A Level Maths: Pure复习笔记5.6.3 R addition formulae Rcos Rsin etc

R addition formulae Rcos Rsin etc

How can I simplify expressions like a sin x ± b cos x  or a cos x ± b sin x?

  • If a and b are positive constants, then
    • sin x + bcos x can be rewritten as R sin (x + α)
    • a sin x - bcos x can be rewritten as R sin (x - α)
    • a cos x + bsin x can be rewritten as R cos (x - α)
    • a cos x - bsin x can be rewritten as R cos (x + α)
  • In all four cases R > 0 and 0 < α < 90°, with:

5.6.3-Rcosxa-Illustr-1

  • To rewrite the expression use the appropriate compound angle formula and equate coefficients

5.6.3-Rcosxa-Illustr-2

Exam Tip

  • There is more than one way to rewrite a given expression, and the question in the exam will tell you which form to use.

Worked Example

5.6.3-Rcosxa-Example

 

 

 

 

 

 

 

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