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Why do we take Sometimes as sinx=x when x is less than 2 or 3

Note by Sudhir Aripirala 3 years, 4 months ago

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When we were learning simple harmonic motion, Our teacher said " For smaller angles sinx=x" How that can be ? @Calvin Lin

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What your teacher meant is that "\( \sin x \approx x \)", where \(x\) is in radians.

This is true because \( \sin x = x - \frac{ x^3 } { 3! } + \frac{ x^5}{ 5!} - \ldots \). So, for small values of \(x\), we have \( \sin x \approx x \).

Ok,thanks sir

Can you explain what you are asking for? I do not understand what you are trying to say by " \( \sin x = x \) when \(x\) is less than 2 or 3."

Another doubt, in the same lesson my teacher also took the condition" For smaller angles sinx=tanx". @Calvin Lin

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`*italics*`

or`_italics_`

italics`**bold**`

or`__bold__`

boldNote: you must add a full line of space before and after lists for them to show up correctlyparagraph 1

paragraph 2

`[example link](https://brilliant.org)`

`> This is a quote`

Remember to wrap math in \( ... \) or \[ ... \] to ensure proper formatting.`2 \times 3`

`2^{34}`

`a_{i-1}`

`\frac{2}{3}`

`\sqrt{2}`

`\sum_{i=1}^3`

`\sin \theta`

`\boxed{123}`

## Comments

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TopNewestWhen we were learning simple harmonic motion, Our teacher said " For smaller angles sinx=x" How that can be ? @Calvin Lin

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What your teacher meant is that "\( \sin x \approx x \)", where \(x\) is in radians.

This is true because \( \sin x = x - \frac{ x^3 } { 3! } + \frac{ x^5}{ 5!} - \ldots \). So, for small values of \(x\), we have \( \sin x \approx x \).

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Ok,thanks sir

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Can you explain what you are asking for? I do not understand what you are trying to say by " \( \sin x = x \) when \(x\) is less than 2 or 3."

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Another doubt, in the same lesson my teacher also took the condition" For smaller angles sinx=tanx". @Calvin Lin

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