Trigonometric Functions

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Trigonometric Functions - Calculate Sine, Cosine, Tangent, and More

Trigonometry is everywhere. It determines the trajectory of a basketball, the angle of a roof truss, the position of a pixel on a circular path, and the frequency response of an audio filter. The Trigonometric Functions tool gives you instant access to all six standard trig functions - sine, cosine, tangent, cosecant, secant, and cotangent - along with their inverse counterparts. Enter an angle, get precise results. No calculator app, no memorised formulas, no rounding mistakes.

The Six Trigonometric Functions

Sine (sin): The ratio of the opposite side to the hypotenuse in a right triangle. In the unit circle, it gives the y-coordinate of a point at angle theta.

Cosine (cos): The ratio of the adjacent side to the hypotenuse. On the unit circle, it is the x-coordinate.

Tangent (tan): The ratio of sine to cosine, or equivalently, opposite over adjacent. Tangent is undefined at 90 degrees and 270 degrees where cosine is zero.

Cosecant (csc): The reciprocal of sine. Undefined where sine is zero.

Secant (sec): The reciprocal of cosine. Undefined where cosine is zero.

Cotangent (cot): The reciprocal of tangent, or cosine divided by sine. Undefined where sine is zero.

Degrees and Radians

Angles can be expressed in degrees or radians, and the tool supports both. Degrees are intuitive for everyday use - a right angle is 90 degrees, a full rotation is 360. Radians are the natural unit in mathematics and physics - a right angle is pi/2, a full rotation is 2pi. Toggle between them freely. The tool converts internally so you never have to do the conversion yourself.

Inverse Trigonometric Functions

Sometimes you know the ratio and need the angle. That is where arcsin, arccos, and arctan come in. Enter a value between -1 and 1 for arcsin or arccos, or any real number for arctan, and the tool returns the corresponding angle. These inverse functions are critical in navigation, physics simulations, and any application where you need to recover an angle from measured quantities.

Who Uses This Tool

Students: Checking homework, preparing for exams, or verifying hand-calculated results. Having a reliable reference prevents small arithmetic errors from cascading through multi-step problems.

Engineers: Structural calculations, signal processing, control systems, and mechanical design all lean heavily on trig functions. A quick lookup tool beats hunting through tables or firing up MATLAB for a single value.

Game developers: Character movement, projectile trajectories, camera rotations, and shader effects use sine and cosine constantly. Prototyping values in this tool before hardcoding them speeds up development.

Graphic designers: Positioning elements along a circular path, creating radial layouts, or calculating rotation transforms for CSS animations all require trig.

Surveyors and navigators: Bearing calculations, distance estimation from angle measurements, and triangulation all depend on trigonometric functions applied to real-world measurements.

Precision You Can Rely On

The tool uses JavaScript's built-in Math functions, which implement IEEE 754 double-precision floating-point arithmetic. Results are accurate to approximately 15 significant digits - more than enough for any practical engineering or scientific calculation. Special values like sin(0) = 0, cos(pi) = -1, and tan(pi/4) = 1 are computed exactly.

No App Required

The Trigonometric Functions calculator runs entirely in your browser. There is no app to download, no registration, and no cost. Bookmark it and use it as your go-to trig reference whenever the need arises.