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

Note by Sudhir Aripirala 2 years, 8 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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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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