The period of the function f(x)= ( 2 3 )+ ( 3 ): - Vidyadip

MCQ

The period of the function $\text{f(x)}=\sin \big(\frac{2\pi\text{x}}{3}\big)+\cos\big(\frac{\pi\text{x}}{3}\big)$:

A
$3$
B
$4$
✓
$12$
D
None of these

✓

Answer

Correct option: C.

$12$

Given, function $\text{f}(\text{x})=\sin \big(\frac{2\pi\text{x}}{3}\big)+\cos \big(\frac{\pi\text{x}}{2}\big)$
Now, period of $\text{f}(\text{x})=\big(\frac{2\pi\text{x}\times{3}}{2\pi}\big)=3$
and period of $\cos \Big(\frac{\text{n}\pi}{2}\Big)=\frac{2\text{n}}{\frac{\text{n}}{2}} = \big(\frac{2\pi\text{}\times{2}}{ \pi}\big)= 2 \times 2 = 4$
Now, period of $f(x) = \text{LCM}(3, 4) = 12$
Hence, period of function $\text{f(x)} = \sin\frac{2\pi\text{x}}{3} + \cos \big(\frac{\pi\text{x}}{2}\big) + \cos$ is $12$

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