Understanding the Inverse Tangent Function | tan^-1(x) and its Importance in Finding Angles

tan^-1(x)

The expression “tan^-1(x)” represents the inverse tangent function

The expression “tan^-1(x)” represents the inverse tangent function.

The tangent function (tan) is a trigonometric function that relates the ratio of the length of the side opposite an angle to the length of the side adjacent to that angle in a right triangle. In other words, for a given angle, the tangent function tells us the slope or steepness of a line that goes through the origin and the point on the unit circle corresponding to that angle.

However, sometimes we want to find the angle itself when given a specific tangent value. This is where the inverse tangent function (or arctan) comes into play. The inverse tangent function “tan^-1” takes a ratio as input and returns the angle whose tangent is equal to that ratio.

For example, if we have tan^-1(1), it means we want to find the angle whose tangent is 1. In this case, the angle is 45 degrees or π/4 radians.

It’s important to note that the inverse tangent function returns an angle within a specific range, typically between -π/2 and π/2 radians (-90 and 90 degrees). This is because tangent is a periodic function and has multiple angles that have the same tangent value. To get all possible angles, we can add or subtract multiples of π (180 degrees) to the base angle.

So, tan^-1(x) gives you the angle whose tangent is x, within a certain range.

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