Sin Cos Tan Calculator

Trigonometric functions describe the relationships between angles and side ratios in a right triangle, but their definition extends well beyond triangles via the unit circle. On a unit circle (radius = 1), an angle θ measured from the positive x-axis determines a point (x, y). At that point, cos(θ) = x and sin(θ) = y. This definition makes trig functions valid for any angle — positive, negative, or greater than 360° — which is essential for analysing periodic phenomena such as sound waves, electrical signals, and planetary motion.

The three primary functions are: sin(θ) = opposite / hypotenuse, cos(θ) = adjacent / hypotenuse, and tan(θ) = opposite / adjacent = sin(θ) / cos(θ). Their reciprocals are cosecant csc(θ) = 1/sin(θ), secant sec(θ) = 1/cos(θ), and cotangent cot(θ) = cos(θ)/sin(θ). All six values together fully characterise the angle's geometric and rotational properties. Note that tan(θ) and sec(θ) are undefined when cos(θ) = 0 (i.e., at 90°, 270°, …), and csc(θ) and cot(θ) are undefined when sin(θ) = 0 (i.e., at 0°, 180°, …).

To use this calculator, enter your angle and select the unit — degrees for everyday geometry and navigation, radians for calculus, physics, and programming. The calculator converts degrees to radians internally using the relation θ_rad = θ_deg × π/180 before applying JavaScript's built-in Math functions, which operate exclusively in radians. Results are displayed to six decimal places for engineering-grade precision. Common reference values to verify results: sin(30°) = 0.5, cos(60°) = 0.5, tan(45°) = 1, sin(90°) = 1.

This calculator uses double-precision floating-point arithmetic (IEEE 754), which introduces tiny rounding errors for angles that are multiples of common reference values. For example, tan(90°) theoretically approaches infinity, but due to floating-point representation of π, the result may be an extremely large number rather than undefined — the calculator handles this by checking if cos(θ) is within 1×10⁻¹⁰ of zero and returning an undefined result. Similarly, sin(180°) may display as approximately −2.45×10⁻¹⁶ rather than exactly 0. For symbolic exact values (e.g., √2/2, √3/2), use a computer algebra system such as Wolfram Alpha. This calculator is designed for numerical approximation, not symbolic computation. It does not solve inverse trig problems (finding the angle from a ratio) — for that, use an arcsin, arccos, or arctan calculator separately.