Trigonometric Identities Question 240
Question: Which of the following functions has period $ 2\pi $ ?
Options:
A) $ y=\sin ( 2\pi t+\frac{\pi }{3} )+2\sin ( 3\pi t+\frac{\pi }{4} )+3\sin 5\pi t $
B) $ y=\sin \frac{\pi }{3}t+\sin \frac{\pi }{4}t $
C) $ y\sin t+\cos 2t $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
We have two functions $ f(x) $ and $ g(x) $ have periods $ T_1 $ and $ T_2 $ respectively, then each of $ f(x)\pm g(x); $ $ f(x).g(x); $ $ f(x)/g(x), $ provided $ g(x)=0 $ has period equal to the LCM of $ T_1 $ and $ T_2 $ . Now, we know that $ sinx $ or $ cosx $ has period $ 2\pi $ Hence period of $ y=\sin t+\cos 2t $ is $ 2\pi $ .
BETA
