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UPSC NDA I 2018 Mathematics Solved Paper

Question : 25 of 120

Marks: +1, -0

What is the period of the function f(x) = sin x?

Solution:

Concept:

A periodic function repeats its values at regular intervals, i.e.,

f(x + T) = f(x)

for some non-zero constant

T

called the period.

Explanation:

We need the period of

f(x) = \sin x

Recall the identity:

\sin(x + 2\pi) = \sin x

for all

x

This means

f(x + 2\pi) = f(x)

. Therefore

2\pi

is a period of

\sin x

No smaller positive constant satisfies this property (since the fundamental period of sine is

2\pi

Answer:

Option D:

2\pi

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