Trigonometric Functions Calculator

At its core, trigonometry connects the angles of a right triangle to the ratios of its side lengths. When you input an angle, the tool first normalizes it into a base angle within a standard 360-degree circle using the modulo operation: base_angle = mod(angle_degrees_print, 360). It converts radians to degrees via angle_degrees_print = angle * 180 / π. From there, it computes primary ratios like sine, cosine, and tangent, along with reciprocal functions including secant, cosecant, and cotangent, applying quadrant checks and oddity rules to ensure mathematical accuracy across all four quadrants.

Let us walk through evaluating the trigonometric functions for an angle of π / 4 radians (which equals 45 degrees). First, the calculator converts this value into degrees: 45°. The base angle remains 45° since it is under 360°. Next, it computes the primary functions: sine and cosine of 45° both evaluate to approximately 0.7071. The tangent is calculated as sin(45°) / cos(45°), yielding exactly 1. Finally, the reciprocal functions are derived: the secant and cosecant are roughly 1.4142, while the cotangent evaluates to 1.

Always verify whether your input parameter is expressed in radians or degrees before running the calculation to avoid massive computational discrepancies. Pay close attention to undefined values, such as the tangent of 90 degrees or cotangent of 0 degrees, where division by zero occurs due to vertical asymptotes.