Question

write the range of the function f(x) = sin [x], where -π/4 \< x\<π/4.​

Answer 1

Given:

function f(x) = sin [x], where -π/4 ≤ x≤π/4.​

To find:

The range of the given function.

Solution:

1) f(x)=sin[x], where   -π/4≤ x≤π/4

The given function is the greatest integer function.

2) The greatest integer function givens the largest value of the function.

3)We divide the range of the given function into two parts,  

-π/4 ≤x≤0

• [x]=−1  ( Greatest integer function)

So the value of the function is:

• f(x)=sin(−1)

•     =−sin1    ( Sin[-x] = -Sinx)

0 ≤ x≤π/4

• [x]=0  ( Greatest  integer function)

So the function is,

• f(x)=sin0=0

hence, the range of f(x) becomes {0,−sin1}

The range of the function f(x) = sin [x], where -π/4 \< x\<π/4 is {0,−sin1}.