Solve sine, cosine, tangent, and reciprocals exactly. Use degrees or radians and compare decimal approximations. Download reports and explore patterns through an interactive graph.
The graph plots the selected function over one full turn and marks the chosen angle when the value exists.
| 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 |
| 315° | 7π/4 | -√2 / 2 | √2 / 2 | -1 |
This calculator uses unit-circle coordinates and special-angle identities. For a point on the circle, sine is the y-coordinate and cosine is the x-coordinate.
Tangent is calculated with tan(θ) = sin(θ) / cos(θ). Cosecant, secant, and cotangent are reciprocal functions whenever their denominators are nonzero.
Exact symbolic output is stored for standard angles spaced by 15 degrees. The calculator normalizes the angle, finds its quadrant, and returns the matching exact expression.
| Time | Function | Input | Normalized Angle | Exact Value | Decimal |
|---|---|---|---|---|---|
| No calculations saved yet. | |||||
This version returns exact symbolic results for multiples of 15 degrees. That includes common unit-circle angles like 0°, 30°, 45°, 60°, 90°, and related coterminal angles.
Yes. You can enter radians such as pi/6, 3pi/4, -pi/3, or decimal radians. The calculator converts them, normalizes the angle, and checks whether an exact symbolic match exists.
A trig value becomes undefined when its denominator is zero. For example, tangent and secant are undefined where cosine equals zero, and cosecant and cotangent are undefined where sine equals zero.
Yes. Stored exact results are already presented in simplified symbolic form, such as √3 / 2 or (√6 - √2) / 4. You do not need extra simplification steps.
Yes. Negative angles are normalized into a coterminal angle between 0° and 360°. The calculator then uses the normalized position to determine the exact value and quadrant.
Exact output keeps the symbolic form, which is useful in algebra and proofs. Decimal output gives a numerical approximation, which is helpful for graphing, checking work, and practical estimates.
The graph shows the selected trig function over one full revolution from 0° to 360°. When the chosen value exists, the selected angle is marked so you can see its position visually.
The export tools include the calculations saved during the current session. Each row contains the function, entered angle, normalized angle, exact result, decimal approximation, and related summary details.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.