What this calculator does
This sin calculator takes an angle, in either degrees or radians, and returns its sine, cosine and tangent together. Those three ratios are the building blocks of trigonometry: given any angle, they describe the shape of a right-angled triangle that has that angle in it, without needing to draw or measure one.
The three are shown together because they are almost always wanted together. A single sine value rarely stands alone in practice: working a triangle, a wave, a slope or a rotation typically needs at least two of the three ratios, so this page computes all three from one angle rather than making three separate lookups.
The formula
Degrees are converted to radians internally with θ_rad = θ_deg × π/180, since the underlying sine, cosine and tangent functions work in radians. Sine and cosine are read straight off the unit circle at that angle; tangent is sine divided by cosine, which is undefined at exactly 90° and 270° (and their radian equivalents), where cosine is zero.
| Term | Meaning |
|---|---|
| sin(θ) | The y-coordinate of the point at angle θ on the unit circle; ranges from −1 to 1. |
| cos(θ) | The x-coordinate of the same point; also ranges from −1 to 1. |
| tan(θ) | sin(θ) ÷ cos(θ); the slope of the line at angle θ, undefined wherever cos(θ) is zero. |
The inputs explained
| Field | What to enter |
|---|---|
| Angle | The angle to evaluate. Negative values and values beyond 360° (or 2π radians) are accepted and handled correctly, since sine and cosine repeat every full turn. |
| Unit | Whether the angle above is in degrees or radians. Switching this does not change the angle itself, only how it is read. |
When to use it
Solving a right-angled triangle
Given one angle and one side, sine and cosine convert that angle into the ratios needed to find the other sides, before any triangle-specific formula is applied.
Checking a slope or gradient
A roof pitch, ramp or road grade expressed as an angle converts directly to a rise-over-run ratio through tangent, without needing to measure rise and run separately.
Working with rotations or waves
Sine and cosine describe circular motion and periodic waves directly, so reading both off a single angle is the first step in modelling a rotation, an oscillation or an AC waveform.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
Sine, cosine and tangent at common angles
The three ratios at angles that come up most often in practice.
| Angle | sin(θ) | cos(θ) | tan(θ) |
|---|---|---|---|
| 0° | 0 | 1.0000 | 0 |
| 30° | 0.500000 | 0.866025 | 0.577350 |
| 45° | 0.707107 | 0.707107 | 1.000000 |
| 60° | 0.866025 | 0.500000 | 1.7321 |
| 90° | 1.0000 | 6.1232e-17 | Undefined (cos = 0) |
| 180° | 1.2246e-16 | -1.0000 | -1.2246e-16 |
| 270° | -1.0000 | -1.8370e-16 | Undefined (cos = 0) |
| 360° | -2.4493e-16 | 1.0000 | -2.4493e-16 |
Questions
What is the difference between this and an arcsin calculator?
This sin calculator goes from an angle to a ratio: enter θ, get sin(θ). The arcsin calculator goes the other way, from a ratio back to the angle that produced it. They are inverse operations, not the same tool.
Why is tangent sometimes "undefined"?
Tangent is sine divided by cosine. At 90° and 270° (and their equivalents every 180° beyond that), cosine equals zero, which makes the division undefined rather than an extremely large or small number.
Does it matter if I enter degrees or radians?
Only in that the angle must be labelled correctly. 90 degrees and π/2 radians describe the same angle and give the same sine, cosine and tangent; entering 90 while the unit is set to radians would evaluate a completely different, much larger angle.
Can the angle be negative or greater than 360°?
Yes. Sine, cosine and tangent are periodic, repeating every 360° (2π radians), and are defined for negative angles too, so any real number is a valid input.
To solve a full triangle from two sides and an angle, or two angles and a side, see the trigonometry triangle solver. To work backwards from a ratio to the angle itself, use the arcsin calculator.