Trigonometric Identities Question 238
Question: Period of the function $ | {{\sin }^{3}}\frac{x}{2} |+| {{\cos }^{5}}\frac{x}{5} | $ is:
Options:
A) $ 2\pi $
B) $ 10\pi $
C) $ 8\pi $
D) $ 5\pi $
Show Answer
Answer:
Correct Answer: B
Solution:
Period of $ \sin x=2\pi $
$ \Rightarrow $ period of $ {{\sin }^{3}}x=2\pi $ period of $ | {{\sin }^{3}}x |=\pi \Rightarrow $ period of $ | {{\sin }^{3}}\frac{x}{2} |=2\pi $ period of $ {{\cos }^{5}}x=2\pi \Rightarrow $ period of $ | {{\cos }^{5}}x |=\pi $
$ \Rightarrow $ period of $ | {{\cos }^{5}}\frac{x}{5} |=5\pi $ Thus required period = LCM of $ 2n $ & $ 5\pi =10\pi $
BETA
