Question

Which could be the graph of the function?

Answer 1

The graph of the function y = sin 0.5x is option A. This can be obtained by using period of the graph function.

Which is the required graph?

Periodic function is a function that repeats at uniform intervals; the time interval between two waves is called the period.

• A function f will be periodic with period n,

f (a + n) = f (a), ∀ n > 0.

After first n the function is same that is f(a), after second function is the same, the function is repeated with an interval of n.

• For example: the period of sin a is 2π  for the reason that the smallest number satisfying sin (a + 2π) = sin a is 2π, for all a.

Therefore the formula for period of a function is 2π/|B| when the function is y = A sin(Bx + C) and y = A cos(Bx + C).

For a function y = sin bx, period is given by,

P = 2π/b

Here function is y = sin 0.5x, therefore b = 0.5

P = 2π/0.5

  =20π/5

  = 4π

Period is 4π. The first graph has period 4π.

Hence the graph of the function y = sin 0.5x is option A.

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Question: Which could be the graph of the function y = sin 0.5x?