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

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