Question

Find the period of the function: cos $(\frac{4x + 9}{5})$

Answer 1

periodic function is a special type of function in which, function returning to the same value at regular intervals. for any function y = f(x) , T will be period only when f(x) = f(x + T).

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

we know, period of cosx = 2π

so, period of cos(4x + 9)/5 or cos(4x/5 + 9/5)

= 2π/(4/5)

= 5π/2

hence, period of function cos(4x + 9)/5 is 5π/2

[ for better understanding, see graph of function attached in answer ]