yr2 chap 7 trigonometry + modelling

• if a problem involves a trigonometric function of (A+B) or (A-B), use the addition formulae in the formula book to expand it, be careful with the signs
• the double angle formulae can be worked out from the addition formulae in the formula book
• sin(2x) = 2 cosx sinx

  cos(2x) = cos^2x - sin^2x = 1 - 2sin^2x = 2cos^2x - 1

  tan(2x) = 2tanx/(1-tan^2x)
• if you are asked to prove any of the double aangle formulae, write them in the form f(x+x) instead of f(2x), then use the addition formulae in the formula book
• to express something in the form $R\sin(x\pm\alpha)$or $Rcos(x\pm\alpha)$, expand that using the addition formulae, then equate the coefficients to find cos alpha and sin alpha, then use the fact that tan = R sin / R cos to find tan alpha and solve for alpha, then square the equated coefficients, put R^2 outside the brackets and use the fact that sin^2x + cos^2x = 1 to solve for R