What is greatest integer function of Sinx?

If sinx is in between 0&1 {sinx}=sinx. First of all draw graph of sinx . Now input of greatest integer function is y (i.e. sinx),Mark all integral y coordinate points on curve and see between any two such point what would be Value of [y], it would be the lesser one of those two.

What is the graph of greatest integer function?

Greatest integer function graph When the intervals are in the form of (n, n+1), the value of greatest integer function is n, where n is an integer. For example, the greatest integer function of the interval [3,4) will be 3. The graph is not continuous. For instance, below is the graph of the function f(x) = ⌊ x ⌋.

How do you graph y Sinx?

Graph of Sinx

1. Draw a Y-axis with 0,1,-1 …on it.
2. From the origin draw an X-axis. a) if you want a graph in π then mark the points π/2, π,3π/2, 2π etc.
3. y = a sin(x) the amplitude ‘a’ is 1 so the curve will be up to (0,1). If y = 2 sin(x) then the amplitude will be 2, so the curve will be up to (0,2).

Is greatest integer function of Sinx continuous?

In the interval [$\dfrac{{3\pi }}{2}$,$2\pi $] , sinx is continuous and its range is [0,-1]. Therefore in the interval ($\dfrac{{3\pi }}{2}$,$2\pi $),[sinx] is continuous and is equal to -1.

Is Sinx discontinuous?

sinx x = 1. The discontinuity of sin(x)/x at x = 0 is removable. We can modify the function to be continuous on the entire real axis by setting f(0) = 1.

How do you write the greatest integer function?

Quick Overview

1. The Greatest Integer Function is also known as the Floor Function.
2. It is written as f(x)=⌊x⌋.
3. The value of ⌊x⌋ is the largest integer that is less than or equal to x.

Where is Sinx not continuous?

As |sin x|/x is equal to sin x/x for 0continuous at 0.

Where is sinx discontinuous?

At x=$2\pi $,[sinx] is equal to 0 therefore it is discontinuous at x=$2\pi $. \end{gathered} }$ [sinx] is discontinuous where n is in integers.

Is sinx continuous everywhere?

The function sin(x) is continuous everywhere.