The Inverse Tangent Function: Definition, Notation, And Examples

Inverse Tan

1/(1+x^2)

The inverse tangent, also known as arctangent, is a trigonometric function that gives the angle whose tangent is a given number. In other words, if we have a value of tan(x), the inverse tangent function will give us the corresponding angle x.

The notation for inverse tangent function is tan⁻¹ or arctan.

If we want to find the angle whose tangent is 1, we can use the arctan function as follows:

tan⁻¹(1) = π/4 or 45 degrees

This means that the angle whose tangent is 1 is 45 degrees.

Similarly, we can find the inverse tangent of any value using a calculator or a table of inverse trigonometric functions. For example:

tan⁻¹(0.5) ≈ 0.464 radians or 26.57 degrees

This means that the angle whose tangent is 0.5 is approximately 0.464 radians or 26.57 degrees.

It is important to note that the arctan function has a restricted domain of (-π/2, π/2), which means it can only provide angles within that range. If the result lies outside that range, we have to add or subtract π until we get an angle within that range.

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