📐 Trigonometry Calculator
Calculate all six trig functions (sin, cos, tan, csc, sec, cot) for any angle, or find the inverse trig values (arcsin, arccos, arctan) for any value. Supports both degrees and radians.
Trig Functions — Enter an Angle
| Function | Formula | Value |
|---|---|---|
| sin θ | opposite / hypotenuse | — |
| cos θ | adjacent / hypotenuse | — |
| tan θ | sin θ / cos θ | — |
| csc θ | 1 / sin θ | — |
| sec θ | 1 / cos θ | — |
| cot θ | cos θ / sin θ | — |
Inverse Trig — Enter a Value
arcsin and arccos require a value between −1 and 1.
SOH-CAH-TOA Explained
Unit Circle Key Angles
| Degrees | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 |
| 30° | π/6 | ½ | √3/2 | 1/√3 |
| 45° | π/4 | √2/2 | √2/2 | 1 |
| 60° | π/3 | √3/2 | ½ | √3 |
| 90° | π/2 | 1 | 0 | undef |
| 180° | π | 0 | −1 | 0 |
| 270° | 3π/2 | −1 | 0 | undef |
| 360° | 2π | 0 | 1 | 0 |
Frequently Asked Questions
In a right triangle, sine (sin) is the ratio of the opposite side to the hypotenuse, cosine (cos) is adjacent over hypotenuse, and tangent (tan) is opposite over adjacent. These ratios depend only on the angle, not the triangle size.
SOH-CAH-TOA is a mnemonic: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. It is the most common way to remember the three primary trig functions.
Both measure angles. A full circle is 360° or 2π radians. To convert degrees to radians multiply by π/180. To convert radians to degrees multiply by 180/π. Radians are the natural unit used in calculus and most scientific contexts.
The unit circle is a circle with radius 1 centred at the origin. For any angle θ, the point on the unit circle is (cos θ, sin θ). It provides a visual way to understand trig values for all angles, including those greater than 90°.
tan θ = sin θ / cos θ. At 90°, cos θ = 0, and division by zero is undefined. Similarly, cot(0°) = cos(0°)/sin(0°) = 1/0, which is undefined. These are called singularities of the trig functions.
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