Trigonometry Calculator: Unit Circle, Sin Cos Tan, Triangle Solver and Graphs
Free trigonometry calculator and simulator: drag the unit circle, get sin, cos, tan, csc, sec and cot with exact values, solve any triangle (SSS, SAS, ASA, AAS and the ambiguous SSA case), graph sinusoids, build trig tables and check identities.
Drag the point around the circle (or use the arrow keys when it is focused); drag any label to move it. sin is the height, cos is the horizontal distance, tan is the length on the tangent line at (1, 0).
Trig functions of an angle
Type in any box: the other two update (like kg and lb in the BMI calculator). Radians accept pi, such as 3pi/4.
Inverse trig: find the angle
Move the pointer over the graph to read values.
Trig table
Identity checker
All the identities
Trigonometry in one page
Trigonometry links the angles of a triangle to the lengths of its sides. In a right triangle: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent (remember SOH-CAH-TOA). The reciprocals are csc = 1/sin, sec = 1/cos and cot = 1/tan. On the unit circle (radius 1), the point at angle θ is (cos θ, sin θ), which extends the functions to every angle, positive or negative.
Special angles
| Angle | Radians | sin | cos | tan |
|---|---|---|---|---|
| 0° | 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 |
The laws for any triangle
Law of sines: a / sin A = b / sin B = c / sin C. Law of cosines: c² = a² + b² − 2ab cos C. Use the Solve triangles tab for SSS, SAS, ASA, AAS and the ambiguous SSA case (two possible triangles).
Questions
- Should my calculator be in degrees or radians?
- Use degrees for everyday angles and geometry; radians (2π = 360°) in calculus and physics. Type 3pi/4 or “2 rad” here and the unit is detected for you.
- Why is tan 90° undefined?
- tan = sin ÷ cos, and cos 90° = 0, so the division by zero has no value; the graph has a vertical asymptote there.
- What is the ambiguous case?
- When you know two sides and an angle that is not between them (SSA), the shorter side can swing to two positions, so there can be two different triangles, one, or none.
- Is my data private?
- Yes. Everything runs in your browser.
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