Sin, Cosine and Tangent Calculator — All Six Trig Ratios
Enter any angle in degrees or radians to instantly see all six trigonometric ratios — sin, cos, tan and their reciprocals csc, sec, cot.
Angle unit
Primary trig ratio — y-coordinate on the unit circle
- 1
Convert to radians
45 × π ÷ 180 = 0.785398 - 2
Compute sin(θ)
sin(0.785398) = 0.707107
How does this calculator work?
Enter any angle (degrees or radians) to get all six trig ratios. sin = y on unit circle, cos = x, tan = sin/cos, and csc = 1/sin, sec = 1/cos, cot = cos/sin. Ratios at undefined points (denominator = 0) are shown as "undefined". All primary ratios stay in [−1, 1].
Formula
How this is calculated
Trigonometric functions relate an angle to the ratios of sides in a right triangle, or equivalently to coordinates on the unit circle. Sine is the y-coordinate (opposite over hypotenuse), cosine is the x-coordinate (adjacent over hypotenuse), and tangent is the slope (opposite over adjacent, equivalently sin ÷ cos). Degree input is converted to radians via rad = θ × π/180 before evaluating.
The three reciprocal functions follow directly: cosecant (csc = 1/sin) is the reciprocal of sine, secant (sec = 1/cos) is the reciprocal of cosine, and cotangent (cot = cos/sin) is the reciprocal of tangent. Any ratio whose denominator is zero — e.g. tan at 90°, sec at 90°, cot at 0° — is mathematically undefined; the calculator displays "undefined" rather than a large floating-point artifact.
IEEE 754 double-precision arithmetic means results at theoretically exact values like sin(180°) may show a tiny residual (around 10⁻¹⁶) instead of exactly zero. This is a property of binary floating-point and not a bug.
Frequently asked questions
In a right triangle: sin = opposite/hypotenuse, cos = adjacent/hypotenuse, tan = opposite/adjacent = sin/cos. On the unit circle: sin is the y-coordinate, cos is the x-coordinate, and tan is the slope of the radius.
They are reciprocals of cos, sin and tan respectively. Wherever the original function equals zero, the reciprocal is 1/0, which is undefined. For example, cos(90°) = 0 so sec(90°) is undefined.
Multiply by π/180. Common values: 30° = π/6 ≈ 0.5236 rad, 45° = π/4 ≈ 0.7854 rad, 90° = π/2 ≈ 1.5708 rad, 180° = π ≈ 3.1416 rad.
TG we-Calculate Editorial Team. (2026). Sin, Cosine and Tangent Calculator — All Six Trig Ratios [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/sin-cosine-tangent-calculator
TG we-Calculate Editorial Team. "Sin, Cosine and Tangent Calculator — All Six Trig Ratios." TG we-Calculate. 2026. https://we-calculate.com/calculator/sin-cosine-tangent-calculator.
TG we-Calculate Editorial Team, "Sin, Cosine and Tangent Calculator — All Six Trig Ratios," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/sin-cosine-tangent-calculator
@misc{wecalculate_sin_cosine_tangent_calculator, title = {Sin, Cosine and Tangent Calculator — All Six Trig Ratios}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/sin-cosine-tangent-calculator}}, year = {2026}, note = {TG we-Calculate} }
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