Home
Class 12
MATHS
Verify that the period of function f(x)...

Verify that the period of function `f(x) =sin^(10)x " is " pi.`

Text Solution

Verified by Experts

We have `f(x)=sin^(10)x`
Now `f(x+pi)=sin^(10)(x+pi)`
`=(sin(x+pi))^(10)`
`=(-sinx)^(10)`
`=sin^(10)x`
`=f(x)`
Thus, we have `f(x+pi)=f(x)` for all ` x in R.`
So,period of f(x) is `pi`.
Promotional Banner

Topper's Solved these Questions

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise Solved Examples|15 Videos

  • RELATIONS AND FUNCTIONS

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 1.1|15 Videos

  • PROPERTIES AND SOLUTIONS OF TRIANGLE

    CENGAGE ENGLISH|Exercise Archives (Numerical Value Type)|3 Videos

  • SCALER TRIPLE PRODUCTS

    CENGAGE ENGLISH|Exercise DPP 2.3|11 Videos

Similar Questions

Explore conceptually related problems

Prove that period of function f(x)=sinx, x in R " is " 2pi.

The period of the function f(x)=sin^(4)3x+cos^(4)3x , is

The period of the function f(x)=sin((2x+3)/(6pi)) , is

The period of the function f(x)=|sin 3x|+| cos 3x| , is

Verify Rolles theorem for function f(x)=sinx-sin2x on [0,\ pi]

Statement-1: The period of the function f(x)=cos[2pi]^(2)x+cos[-2pi^(2)]x+[x] is pi, [x] being greatest integer function and [x] is a fractional part of x, is pi . Statement-2: The cosine function is periodic with period 2pi

The period of f(x)=sin(sin(x/5)) , is

Verify Rolle's theorem for the following function f(x)=e^(-x) sin x in [0,pi]

Verify Rolles theorem for function f(x)=sin^4\ x+cos^4\ x on [0,\ pi/2]

In each of the following cases find the period of the function if it is periodic. (i) f(x)="sin"(pi x)/(sqrt(2))+"cos"(pi x)/(sqrt(3)) " (ii) " f(x)="sin"(pi x)/(sqrt(3))+"cos"(pi x)/(2sqrt(3))