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Maths-

General

Easy

Question

The cosecant function whose period is 4 is

$cosec \frac{π x}{3}$
$cosec \frac{2 π x}{5}$
$cosec 2 π x$
$cosec \frac{π x}{2}$

hint Hint:

In this question, period of a cosecant function is given we have to find the cosecant function. For this we know that fundamental period of cosecant $open vertical bar k close vertical bar$ is $fraction numerator 2 straight pi over denominator open vertical bar k close vertical bar end fraction$ . So, using this we can find the value of k and get the cosecant function.

The correct answer is: $cosec space fraction numerator pi x over denominator 2 end fraction$

f(x)=cosecx
period of f(x)=4
We know that period of cosec $open vertical bar k close vertical bar$ = $fraction numerator 2 straight pi over denominator open vertical bar k close vertical bar end fraction$
$rightwards double arrow fraction numerator 2 straight pi over denominator open vertical bar k close vertical bar end fraction equals 4 rightwards double arrow open vertical bar k close vertical bar equals straight pi over 2$
So, cosecant function whose period is 4 is cosec $open parentheses πx over 2 close parentheses$ .

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