Understanding the Inverse Tangent Function | Notation and Application

y = tan⁻¹ u/a

In mathematics, the notation “tan⁻¹” represents the inverse tangent function, also known as the arctangent function

In mathematics, the notation “tan⁻¹” represents the inverse tangent function, also known as the arctangent function. When used in the expression y = tan⁻¹(u/a), it means that y is the angle (in radians or degrees) whose tangent is u/a.

Let’s break down the meaning of each component in the expression:

– “tan⁻¹” or “arctan” refers to the inverse tangent function. It is the opposite operation of taking the tangent of an angle. In general, if we have y = tan(x), then “tan⁻¹(y)” or “arctan(y)” would give us the angle x.

– “u” and “a” are variables. Typically, “u” and “a” represent numbers, but they can also represent algebraic expressions or variables themselves.

Therefore, the expression y = tan⁻¹(u/a) states that y is the angle whose tangent is the ratio of u to a. This ratio can be thought of as the height (u) over the adjacent side (a) in a right-angled triangle.

To find the value of y, you can use the inverse tangent function on a calculator or math software that supports trigonometric functions. Take the ratio u/a and compute its inverse tangent using your preferred mode (degrees or radians) to determine the angle y.

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