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**o_O** Let $\displaystyle \theta = \tan^{-1} x \ \Leftrightarrow \ \tan \theta = \frac{x}{1} = \text{"} \frac{\text{opp}}{\text{adj}} \text{"}$

So construct a right triangle with angle $\displaystyle \theta$ such that the side opposite it has length $\displaystyle x$ and the side adjacent it is $\displaystyle 1$. By the Pythagorean theorem, the hypotenuse must be $\displaystyle \sqrt{x^2 + 1}$

So what does $\displaystyle \sin \theta$ equal to? What was $\displaystyle \theta$ in the first place?