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I am learning the proof for the Special Trigonometric Limit.

$\lim_{x \to 0} \dfrac{\sin x}{x} = 1$

But I have a basic Geometry question I can't figure out. Why is the side of the smaller triangle = $\sin(\theta)$? (See the marker highlighted side).

Is it a trigonometry property? If so, what is the name? I would like to learn how it works and how to derive it. (I am not sure)... But in my case, is this a $45-45-90$ triangle? I have a feeling it might be related? If so, does it only work on $45-45-90$ triangle?

Please see the smaller triangle marked side

N. F. Taussig
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George
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    Because from its definition $\sin(\theta)=\frac{opposite}{hypotenuse}$ and in this case the hypotenuse is equal to one. Look careful where it says "Draw a unit circle" - that means a circle of radius 1. – Mufasa Jan 18 '15 at 21:58

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$\operatorname{sine}(\theta) = \dfrac{\text{opposite}}{\text{hypotenuse}} = \dfrac{\text{opposite}}{\text{radius}} = \dfrac{\text{opposite}}{1}$

because we're dealing with the unit circle.

Edit: you have a typo, fourth line from the bottom, it should be $\dfrac {\sin \theta}{\theta} = \dfrac {\sin(-\theta)}{-\theta}$

GFauxPas
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