Express 2cos(x) + 5sin(x) in the form Rsin(x + a) where 0<a<90

Expanding Rsin(x + a): Rsin(x + a) = Rsin(x)cos(a) + Rcos(x)sin(a) Comparing coefficients of sin(x), cos(x) with first expression leads to: Rsin(a) = 2, Rcos(a) = 5 Dividing these equations gives: tan(a) = 2/5 therfore a = arctan(2/5) Squaring and adding these equations gives: R^2(sin^2(a) + cos^2(a)) = 2^2 + 5^2 therefore R = root(29)