Tangent Calculator

Tangent is a trigonometric function that relates an angle to a ratio. In a right triangle, the tangent of an acute angle is the length of the opposite side divided by the length of the adjacent side. On the unit circle, tangent is sine divided by cosine. This second definition extends naturally to positive, negative, and large angles and explains why tangent repeats every 180 degrees or every pi radians. The tangent mode treats the entered number as an angle. When degrees are selected, the calculator converts that angle to radians before evaluating the standard tangent function. When radians are selected, it uses the number directly. Because tangent divides by cosine, it is undefined where cosine is zero. The calculator detects values whose converted cosine is extremely close to zero and reports an undefined result rather than displaying a huge unstable floating-point number near odd multiples of 90 degrees. Arctangent is the inverse operation. It starts with a ratio or slope and returns the principal angle whose tangent has that value. Its principal output lies strictly between negative 90 and positive 90 degrees, or between negative one-half pi and positive one-half pi radians. In arctangent mode, the unit choice controls the output angle rather than changing the input value. For example, an input of one returns 45 degrees or approximately 0.785398 radians. Tangent is widely used to calculate slopes, heights, distances, bearings, roof pitches, camera fields of view, and components of forces. Arctangent converts a known rise-over-run ratio into an angle and appears in navigation, surveying, vector analysis, robotics, graphics, and engineering. When signs of both horizontal and vertical coordinates matter, a two-argument arctangent is often preferable because it identifies the correct quadrant; this single-value calculator implements the ordinary one-argument inverse tangent. Results are rounded to six decimal places and tiny values near zero are displayed as zero. Always verify the selected unit, since tangent of 45 degrees differs completely from tangent of 45 radians. Also remember that a rounded decimal is a numerical approximation for most angles. Exact values and symbolic multiples of pi can be more informative in algebraic work, while this calculator is intended for quick deterministic numeric evaluation.