What is the period of f(x)=sin(x)

Period is the amount that goes from one peak to the next or from any point to the next matching point, i.e when the value of the function again becomes the same as it was before.

We know that for [tex]y=a\sin\ (bx+c)+d[/tex], the period will be

[tex]\text{Period}=\dfrac{2\pi}{|b|}[/tex]

As in the given case, b=1 so period will be

[tex]\text{Period}=\dfrac{2\pi}{|1|}=\dfrac{2\pi}{1}=2\pi[/tex]

snehapa snehapa · Answer 2 · 2019-10-16T21:01:54+02:00

The period of [tex]f\left(x\right)=\sin x[/tex] is [tex]\boxed{2\pi }[/tex] .

Further explanation:

The general equation of the sine function is given by,

[tex]\boxed{y=a\times\sin\left({bx+c}\right)}[/tex]

Here, a represents as the amplitude of the function, b represents the frequency and c represents the phase.

Given:

The function is [tex]f\left(x\right)=\sin\left(x\right)[/tex].

Explanation:

The period of a function is defined as in the interval the value of the function repeated in both the direction.

The sine function is a periodic function.

The period of function [tex]f\left(x\right)=\sin\left(x\right)[/tex] can be obtained as follows,

[tex]{\text{Period}}=\frac{{2\pi }}{{\left|b\right|}}[/tex]

Compare the general equation of sine function [tex]{y=a\times\sin\left({bx+c}\right)}[/tex] with the equation [tex]f\left(x\right)=\sin\left(x\right)[/tex].

The value of b is 1.

The period can be obtained as follows,

[tex]\begin{aligned}{\text{Period}}&=\frac{{2\pi}}{1}\\&=2\pi\\\end{aligned}[/tex]

Hence, the period of [tex]f\left(x\right)=\sin x[/tex] is [tex]\boxed{2\pi }[/tex].

Kindly refer to the image attached.

Learn more:

1. Learn more about inverse of the function https://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Trigonometry

Keywords: quadrants, angle, expression, sin x, period, amplitude, peak point, phase, maximum value of sin x.