Find the maximum value of 2sin(x)-1.5cos(x)

Put the equation in the form Rsin(x-a) (=Rsin(x)cos(a)-Rcos(x)sin(a)). Looking at the original equation Rcos(a) = 2 and Rsin(a) = 1.5. Tan(a)=1.5/2 and R^2= 2^2 +1.5^2. Therefore R = 2.5 and a = 0.6435.The max value of 2.5 sin(x - 0.6435) = 2.5 and occurs when x = 2.2143 (4 d.p)