Question

Find the period for the function: 2 sin ($\frac{\pi x}{4}$) + 3 cos ($\frac{\pi x}{3}$)

Answer 1

we know , if T is the period of function y = f(x) Then, T/|a| will be the period of function y = f(ax ± b)

it is known that period of sinx = 2π

so, period of sin(πx/4) = 2π/(π/4) = 8

also it is known that period of cosx = 2π

so, period of cos(πx/3) = 2π/(π/3) = 6

now, Period of 2 sin ($\frac{\pi x}{4}$) + 3 cos ($\frac{\pi x}{3}$) = LCM { period of sin(πx/4) , period of cos(πx/3) }

= LCM { 8, 6}

= 24

hence, period of given function is 24.