The Inverse Tangent Function And How To Find Angles In Right Triangles.

tan^-1(x)

1/(1+x^2)

The notation tan^-1(x) (sometimes written as arctan(x) or atan(x)) represents the inverse tangent function. It is an inverse trigonometric function that takes a ratio of two sides of a right triangle (opposite over adjacent) and returns the angle whose tangent is that ratio.

For example, if we have a right triangle with opposite side length 3 and adjacent side length 4, then the tangent of the angle opposite the 3 side is 3/4. Using the inverse tangent function, we can find the measure of that angle:

tan^-1(3/4) = 36.87 degrees

So the angle opposite the 3 side has a measure of approximately 36.87 degrees.

Note that the inverse tangent function is limited in its range. It can only return angles between -90 degrees and 90 degrees, because those are the only angles whose tangent values fall within the range of the tangent function (-infinity to +infinity). If you need to find an angle outside of that range, you will need to account for the quadrant of the triangle in which the angle lies, and adjust your answer accordingly.

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