First slide

Functions (XII)

Question

Which of the following functions has period $π$ ?

Moderate

A

$2 \cos (\frac{2 πx}{3}) + 3 \sin (\frac{πx}{3})$
B

|tan x| + cos 2x
C

$4 \cos (2 πx + \frac{π}{2}) + 2 \sin (πx + \frac{π}{4})$
D

None of these

Solution

$Period of 2 \cos (\frac{2 πx}{3}) + 3 \sin (\frac{πx}{3}) = L.C.M. (\frac{2 π}{2 π / 3}, \frac{2 π}{π / 3}) = 6 Period of 4 \cos (2 πx + \frac{π}{2}) + 2 \sin (πx + \frac{π}{4}) = L.C.M. (\frac{2 π}{2 π}, \frac{2 π}{π}) = 2 Period of | \tan x | + \cos 2 x = L.C.M. (π, \frac{2 π}{2}) = π$

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