$\displaystyle \large \lim_x \,\to\, 0\normalsize \dfrac\sinxx \,=\, 1$

The limit of ratio of sin of angle to angle as the angle viewpoints zero is equal to one. This standard an outcome is used as a dominance to evaluate the limit of a duty in which sine is involved.

You are watching: Lim x approaches 0 sinx x


$x$ is a variable and also represents angle of a right triangle. The sine role is written as $\sinx$ together per trigonometry. The limit of quotient the $\sinx$ through $x$ together $x$ approaches zero is often appeared in calculus.

$\displaystyle \large \lim_x \,\to\, 0\normalsize \dfrac\sinxx$

Actually, the limit of $\sin(x)/x$ together $x$ has tendency to $0$ is same to $1$ and also this traditional trigonometric function result is provided as a formula almost everywhere in calculus.


There room two means to prove this limit of trigonometric function property in mathematics.

Relation between Sine duty and angle

It is derived on the communication of nearby relation between $\sinx$ role and edge $x$ as the angle $x$ closer to zero.

Learn Proof
Taylor (or) Maclaurin series Method

It can also be acquired by the expansion of $\sinx$ function as every Taylor (or) Maclaurin series.

Learn Proof
Latest mathematics Topics
Sep 14, 2021
Equality building of identify integrals
Sep 11, 2021
Introduction to the greater than symbol v examples
Sep 03, 2021
Proof of Equality home of definite integrals
Aug 28, 2021
Addition ascendancy of inequalities with basic examples
Aug 25, 2021
Introduction to the Non-strict inequalities with examples
Latest math Problems
Sep 17, 2021
Evaluate $\dfrac3\sin3x+2\cos(2x+5^\circ)2\cos3x-\sin(2x-10^\circ)$ if $x = 20^\circ$
Sep 12, 2021
Solve $\log_5-x(x^2-2x+65) = 2$
Sep 07, 2021
Factorize $x^4+64$
Sep 06, 2021
Evaluate $\displaystyle \int\dfrac2x+3x^2+4x+5\,dx$
Sep 05, 2021
Evaluate $\sqrt3\csc20^\circ-\sec20^\circ$

A best cost-free mathematics education and learning website because that students, teachers and researchers.

Maths Topics

Learn every topic that the mathematics conveniently with understandable proofs and also visual animation graphics.

Maths Problems

Learn exactly how to solve the maths troubles in various methods with understandable steps.

See more: How Do You Make A Bow And Arrow In Minecraft, Make A Bow And Arrow In Minecraft

Learn solutions

Subscribe us

You can gain the recent updates from united state by adhering to to our official page of math Doubts in one of your favourite social media sites.