Maths-
General
Easy
Question
The period of f(x) = [sin 5x] + |cos 6x| is -
- 2
Hint:
In this question we have to find the period of f(x) = [sin 5x] + |cos 6x|. Here [.] is greatest integer function and | is modulus function. Find the each individual function’s period and then take LCM of both function .
The correct answer is: 2
Here we have to find the solution of period of f(x) = [sin5x] + |cos 6x|.
Firstly, we are given two function, first is greater integer function and second is modulus function.
We have, f(x) = [sin 5x] + |cos 6x|
f(x) = f1(x) + f2(x)
For greater integer function,
f1(x) = [sin 5x]
period of f1(x) = [sin 5x]
we know that the period of sinx → 2π
period of [sin 5x] = [sin ( 5x + 2π) ]
period of f1(x) = [sin 5 ( x + 2π/5)]
therefore the period of f1(x) = 2 π/5 =
For modulus function,
f2(x) = | cos 6x |
we know that period of cosx → π
period of f2(x) = |cos 6x| = |cos 6x + π|
= |cos 6( x + π/6)|
Therefore, Period of f2(x) = π/6
Now, LCM of 2 π/5 and π/6 = 2π
Therefore, the correct answer is 2π.
In this question , we have to find the period of f(x) = [sin 5x] + |cos 6x|. We know that sinx period is 2 π and cosx is π. we know that if sin(x + a) then a is period so find the a both in sin and cos and then take both LCM.
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