Formula

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

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.

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Introduction

$x$ 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.

Proof

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.


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Taylor (or) Maclaurin series Method

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


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