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
- a 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:
- To rewrite the expression use the appropriate compound angle formula and equate coefficients
- There is more than one way to rewrite a given expression, and the question in the exam will tell you which form to use.