Sine Cosine Calculator Form
This tool accepts negative angles, large rotations, and either degree or radian input.
Plotly Graph
The graph shows sine and cosine curves on a degree-based axis. The selected angle is marked on both curves after calculation.
Example Data Table
| Angle | Radians | sin(θ) | cos(θ) |
|---|---|---|---|
| 0° | 0 | 0 | 1 |
| 30° | π/6 | 1/2 | √3/2 |
| 45° | π/4 | √2/2 | √2/2 |
| 60° | π/3 | √3/2 | 1/2 |
| 90° | π/2 | 1 | 0 |
| 180° | π | 0 | -1 |
Formula Used
Sine ratio: sin(θ) = opposite / hypotenuse
Cosine ratio: cos(θ) = adjacent / hypotenuse
Unit circle point: (x, y) = (cos(θ), sin(θ))
Pythagorean identity: sin²(θ) + cos²(θ) = 1
Degree to radian conversion: radians = degrees × π / 180
Radian to degree conversion: degrees = radians × 180 / π
How to Use This Calculator
- Enter the angle value in the first field.
- Select degrees or radians as the input unit.
- Choose whether to highlight sine, cosine, or both.
- Set the decimal precision for the final answers.
- Choose how many coterminal pairs you want listed.
- Press Calculate Now to view the result above the form.
- Review the values, coterminal angles, and graph marker.
- Use the export buttons to save the result as CSV or PDF.
Frequently Asked Questions
1. What does this sine cosine calculator do?
It calculates sine and cosine values from a given angle. It also converts units, normalizes rotations, identifies the quadrant, and lists coterminal angles.
2. Can I enter radians instead of degrees?
Yes. Select radians in the unit menu, enter your value, and the tool will calculate sine and cosine while also showing the equivalent degree measure.
3. Why are sine and cosine between -1 and 1?
On the unit circle, cosine is the x-coordinate and sine is the y-coordinate. Coordinates on that circle cannot go beyond 1 or below -1.
4. What is a coterminal angle?
A coterminal angle ends at the same terminal side after full rotations. You get one by adding or subtracting 360° or 2π radians.
5. What is the reference angle?
The reference angle is the smallest positive angle between the terminal side and the x-axis. It helps determine sine and cosine signs.
6. Why does the tool show normalized angles?
Normalized angles place any input within one complete turn. This makes quadrant checks, graph reading, and comparison much easier.
7. Does the identity sin²(θ) + cos²(θ) always equal 1?
Yes. For every real angle, the Pythagorean identity holds. Minor decimal differences only happen because computers round long floating-point numbers.
8. Can I download the output?
Yes. After calculation, use the CSV or PDF buttons to save the summary table and coterminal angle table for later reference.