Trigonometry Calculator – Sin, Cos, Tan & Inverse Functions

Sine (sin), cosine (cos), and tangent (tan) are the three primary trigonometric functions. In a right triangle, sin(θ) = opposite/hypotenuse, cos(θ) = adjacent/hypotenuse, and tan(θ) = opposite/adjacent = sin(θ)/cos(θ). On the unit circle, sin is the y-coordinate and cos is the x-coordinate of a point at angle θ. These functions are fundamental in mathematics, physics, engineering, and computer graphics.

Degrees and radians are two ways to measure angles. 360° = 2π radians. One radian is the angle subtended by an arc equal in length to the radius (≈57.2958°). To convert: radians = degrees × π/180, and degrees = radians × 180/π. Radians are preferred in calculus and advanced mathematics because they simplify derivative formulas (e.g., d/dx[sin(x)] = cos(x) only when x is in radians).

SOHCAHTOA is a mnemonic for remembering the three primary trig ratios in a right triangle:
• SOH: Sin = Opposite / Hypotenuse
• CAH: Cos = Adjacent / Hypotenuse
• TOA: Tan = Opposite / Adjacent
This only works for right triangles. For general triangles, use the Law of Sines and Law of Cosines.

Inverse trig functions (arcsin, arccos, arctan) find the angle given a trigonometric ratio. For example, arcsin(0.5) = 30° because sin(30°) = 0.5. Key facts:
• arcsin(x): domain [-1, 1], range [-π/2, π/2] (or [-90°, 90°])
• arccos(x): domain [-1, 1], range [0, π] (or [0°, 180°])
• arctan(x): domain (-∞, ∞), range (-π/2, π/2) (or (-90°, 90°))
They are essential for solving equations like sin(θ) = 0.7 and finding θ.

Since tan(θ) = sin(θ)/cos(θ), when cos(θ) = 0, the denominator becomes zero, making the expression undefined. At 90° (π/2 rad), cos(90°) = 0 while sin(90°) = 1, so tan(90°) = 1/0, which is undefined (the limit approaches ±∞). Similarly, cot(0°) is undefined because sin(0°) = 0. This calculator shows "Undefined" when the result would involve division by zero.

Trigonometry is used extensively in:
• Engineering: structural analysis, signal processing, AC circuit design
• Physics: projectile motion, wave mechanics, optics
• Computer Graphics: 3D rotations, camera transforms, game development
• Navigation: GPS triangulation, flight paths, maritime navigation
• Architecture: roof pitch calculation, structural load analysis
• Music & Audio: sound wave synthesis, frequency analysis

This calculator uses JavaScript's built-in Math.sin(), Math.cos(), Math.tan(), Math.asin(), Math.acos(), and Math.atan() functions, which comply with the IEEE 754 floating-point standard. Results are displayed to 6 decimal places, providing more than sufficient precision for most educational, engineering, and everyday applications. For critical scientific computations, specialized high-precision libraries may be preferred.