First slide

Functions (XII)

Question

A function out of the following whose
period is not $π$ is

Moderate

A

$\sin^{2} x$
B

$\cos^{2} x$
C

$\tan (2 x + 3)$
D

$y = | \sin x |$

Solution

$y = \sin^{2} x = \frac{1}{2} [1 - \cos 2 x]$ Since period of $\cos x is 2 π$ so period of $\cos 2 x is π .$
$y = 1 + \cos^{2} x = 1 + \frac{1}{2} (1 + \cos 2 x)$ The period of this is
again $π$ The period of tan $x$ is p so period of tan $(2 p + 3)$ is
$π / 2 .$ If $f (x) = | \sin x |$ then $f (x + p) = | \sin (x + p) | = | - \sin x | =$
$\sin x Á = f (x) .$ Thus the period of $f$ is $π$

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