Question

what is the period of cos (4x+5)​

Answer 1

SOLUTION

TO DETERMINE

The period of

$\sf{ \cos (4x + 5)}$

CONCEPT TO BE IMPLEMENTED

1. A function f (x) is said to be a periodic function of period T if

$\sf{f(x + T) = f(x)}$

2. If f(x) is a periodic function of period T then period of f(ax+b) is

$\displaystyle \sf{ = \frac{T}{ |a| } }$

EVALUATION

Here the given function is

$\sf{ \cos (4x + 5)}$

$\sf{Now \: the \: period \: of \: \cos x \: \: is \: \: 2\pi}$

$\sf{ \therefore \:The \: period \: of \: \cos (4x + 5)\: \: is \: \: }$

$\displaystyle \sf{ = \frac{Period \: of \: \cos x }{Coefficient \: of \: \: x} }$

$\displaystyle \sf{ = \frac{2\pi }{4} }$

$\displaystyle \sf{ = \frac{\pi }{2} }$

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