The three basic trig ratios — sine, cosine, and tangent — evaluated directly for any angle, in degrees or radians.
How it works
The angle is converted to radians if entered in degrees, then the standard sine, cosine, and tangent functions are evaluated directly.
What this does not include
This does not include solving a triangle from side lengths — for that, use this site’s right-triangle side-and-angle calculator or hypotenuse calculator instead.
How to use this calculator
- Enter an angle and choose degrees or radians.
A worked example
At 30°: sin = 0.5, cos = 0.8660, tan = 0.5774.
At 90°: sin = 1, cos = 0, and tan is undefined — division by cos(90°) = 0 has no result.
What the variables mean
| Variable | Meaning |
|---|---|
| Angle | The input angle, in degrees or radians |
| sin, cos, tan | The three basic trigonometric ratios for that angle |
Edge cases worth knowing
Tangent is undefined at 90° (and 270°) — since tan = sin/cos, and cos is zero at those angles, the calculator correctly shows no value rather than a nonsensical number.
Degrees and radians give the same underlying ratios, just different input scales — 30° and π/6 radians describe the identical angle, so switching units shouldn’t change the sin, cos, or tan output.
Frequently asked questions
Why is tangent undefined at 90 degrees?
Tangent is sine divided by cosine, and cosine of 90 degrees is zero — division by zero has no defined result, so tangent is undefined at that angle.
What’s the difference between degrees and radians?
Degrees divide a full circle into 360 parts; radians measure angle by arc length relative to the radius, with a full circle equal to 2π radians.
Where are these three ratios most commonly used?
Solving right triangles, physics problems involving angles and forces, and engineering calculations involving rotation or waves.
