Tangent calculator

Tangent is a trigonometric function that relates the ratio of the length of the opposite side to the length of the adjacent side in a right-angled triangle. In a right triangle with one angle as the reference angle, the tangent of that angle is defined as the length of the opposite side divided by the length of the adjacent side.

Mathematically, the tangent function is denoted as "tan" and is defined as follows:

tan(angle) = opposite / adjacent

In a unit circle, the tangent of an angle can also be defined as the y-coordinate of the point on the unit circle corresponding to that angle divided by the x-coordinate.

The tangent function has a range that spans from negative infinity to positive infinity. It is positive in the first and third quadrants, and negative in the second and fourth quadrants. The tangent function is periodic with a period of 180 degrees (or π radians), meaning that it repeats its values after every 180 degrees (or π radians).

The tangent function is widely used in trigonometry, calculus, physics, engineering, and many other fields to model and analyze the relationship between angles and sides in triangles, as well as in the study of periodic phenomena and waveforms. It is an important function in various mathematical calculations and applications.

The tangent formula, also known as the tangent identity, is a trigonometric equation that relates the tangent of the sum or difference of two angles to the tangents of the individual angles. There are two main tangent formulas: the tangent addition formula and the tangent subtraction formula.

Tangent Addition Formula: The tangent addition formula states that the tangent of the sum of two angles (A + B) is equal to the sum of the tangents of the individual angles divided by 1 minus the product of their tangents.

tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A) * tan(B))

Tangent Subtraction Formula: The tangent subtraction formula states that the tangent of the difference of two angles (A - B) is equal to the difference of the tangents of the individual angles divided by 1 plus the product of their tangents.

tan(A - B) = (tan(A) - tan(B)) / (1 + tan(A) * tan(B))

These formulas are useful in trigonometry for simplifying or evaluating trigonometric expressions involving sums or differences of angles. They can be derived from the definitions of sine and cosine using basic trigonometric identities.

It's important to note that these formulas assume that the tangents of the individual angles are defined and the denominators are not zero. Division by zero is undefined, so caution should be taken when applying these formulas.