A free trigonometry calculator with three tools in one: find sin, cos, tan and their reciprocals (with exact values, quadrant and reference angle), solve a right triangle from any two values, or solve any triangle with the law of sines and cosines, including the tricky SSA ambiguous case.
Enter any two values (at least one side). C is the right angle and c is the hypotenuse.
Enter any three values, including at least one side. Side a is opposite angle A, b opposite B, c opposite C.
Trig formulas this calculator uses
Exact values of special angles
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° (π/6) | 1/2 | √3/2 | √3/3 |
| 45° (π/4) | √2/2 | √2/2 | 1 |
| 60° (π/3) | √3/2 | 1/2 | √3 |
| 90° (π/2) | 1 | 0 | undefined |
For any other angle, find its reference angle (the acute angle to the x-axis) and apply the sign for its quadrant: All positive in Quadrant I, Sin in II, Tan in III and Cos in IV (“All Students Take Calculus”). So sin 150° = +sin 30° = 1/2 and cos 150° = −cos 30° = −√3/2.
Solving any triangle: which law to use
- SSS (three sides) or SAS (two sides and the angle between them): start with the law of cosines.
- ASA or AAS (two angles and a side): find the third angle (angles add to 180°), then use the law of sines.
- SSA (two sides and a non-included angle): the ambiguous case. There can be zero, one or two triangles, and this calculator shows every valid one.
Frequently asked questions
How do I find sin, cos and tan of an angle?
Enter the angle, choose degrees or radians and press Calculate. You get all six trig ratios as decimals, the exact surd form for special angles like 30°, 45° and 60°, plus the quadrant and reference angle.
How do I solve a right triangle?
Choose Right triangle and enter any two values with at least one side, for example two legs, or a leg and an angle. The calculator uses Pythagoras and SOH CAH TOA to find the other sides, angles, area and perimeter.
When do I use the law of sines vs the law of cosines?
Use the law of cosines when you know three sides (SSS) or two sides and the angle between them (SAS). Use the law of sines when you know two angles and a side (ASA, AAS) or two sides and a non-included angle (SSA).
What is the ambiguous case (SSA)?
When you know two sides and an angle that is not between them, the data can fit two different triangles, one triangle or none. The calculator checks sin B = b·sin A / a and lists every valid solution.
Why does tan 90° show as undefined?
tan = sin/cos, and cos 90° = 0, so you would be dividing by zero. The same is true for sec 90°, and for csc and cot at 0° and 180°.
Related tools
Free educational tool by HawkInc. Results are calculated in your browser and rounded for display; check critical work by hand or with a second method.