Understanding Trigonometry: Explanation of the Inverse Tangent Function

[DivGradCurl]

I have a straight-forward question. Could anybody please explain me why...

\theta = \tan ^{-1} \left( \frac{x}{2} \right) \Rightarrow -\frac{1}{4\sin \theta} = -\frac{\sqrt{x^2+4}}{4x}

Thanks

 

[whozum]

Draw a triangle. Your vertical side will be x, your horizontal base will be 2. This is directly from the tan function. From there you can use pythagorean theorem to find the hypotenuse. Now you have all three sides, and you're trying to find

-4csc(\theta). Just pull it right off the triangle. CSC is hyp/opp.

 

[DivGradCurl]

One sec. after I posted it I realized what to do. Thanks, anyway.