Question

Find the period of the function cos(4x+9/5)

Answer 1

we have to find period of the function cos(4x + 9/5)

concept : if period of function y = f(x) ihen, period of function y = f(ax) is T/|a|

period of function y = f(x ± c) is T

period of function y = f(ax ± c) is T/|a|

period of function y = f(x/a ± c) is |a|T

we know, period of cosx is 2π

then, period of cos(4x) = 2π/|4| = π/2

and also period of cos(4x + 9/5) = π/2

hence, period of cos(4x + 9/5) = π/2

Answer 2

Answer:

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 ]