Advanced Cosine Calculator

Solve cosine, inverse cosine, and triangle relations accurately. Choose degrees, radians, grads, or DMS easily. Review charts, examples, formulas, and downloadable result tables instantly.

Cosine calculator

Calculation mode

Decimal precision

Nearby table points Odd values work best for a centered table.

Angle unit

Output angle unit

Nearby step Use the same unit as your current mode.

Angle input Examples: 60, 1.0472, or 30 15 10 for DMS.

Cosine value Valid range: -1 to 1.

Side a

Side b

Included angle C Supports degrees, radians, gradians, or DMS input.

Side c Angle C is opposite side c.

Example data table

Angle	Radians	cos(x)	Common use
0°	0	1	Maximum cosine value
30°	π/6	0.866025	Special-angle triangle work
45°	π/4	0.707107	Symmetry and diagonal problems
60°	π/3	0.5	Reference-angle checks
90°	π/2	0	Perpendicular direction tests

This sample table helps verify expected answers before you test custom values, triangle inputs, or inverse cosine cases.

Formula used

Standard cosine: cos(x)

Inverse cosine: x = arccos(v), where -1 ≤ v ≤ 1

Law of cosines for a side: c² = a² + b² - 2ab cos(C)

Law of cosines for an angle: cos(C) = (a² + b² - c²) / (2ab)

Secant: sec(x) = 1 / cos(x), when cos(x) ≠ 0

Area from two sides and included angle: Area = ½ab sin(C)

How to use this calculator

Select the calculation mode that matches your problem.
Choose the needed angle unit or output unit.
Enter the angle, cosine value, or triangle sides.
Set precision, nearby step, and nearby table points.
Press Calculate to show the result above the form.
Review the summary, nearby values table, and the Plotly graph.
Use the CSV or PDF buttons to export results.

FAQs

1) What calculation modes are included?

This tool handles direct cosine, inverse cosine, solving a side with the law of cosines, and solving an angle from three sides.

2) Which angle units can I use?

You can work in degrees, radians, gradians, and DMS for direct angle input. Output angles for inverse and triangle angle solving can be shown in degrees, radians, or gradians.

3) How do I enter DMS values?

Enter DMS as degrees only, degrees and minutes, or degrees minutes seconds. Examples: 30, 30 15, or 30 15 10.

4) Why is inverse cosine limited to values from -1 to 1?

Cosine outputs never go below -1 or above 1 for real angles. Because of that, arccos can only accept inputs inside this interval.

5) Why does sec(x) sometimes show as undefined?

Secant is the reciprocal of cosine. When cosine equals zero, division by zero would occur, so secant has no real finite value.

6) When should I use the law of cosines?

Use it when you know two sides and the included angle, or when all three sides are known and you need a specific angle.

7) What is the nearby values table for?

It shows how the result changes around your chosen input. That helps with checking trends, sensitivity, and quick comparisons before exporting.

8) Can I export the calculated results?

Yes. After calculation, use the built-in CSV button for spreadsheet work or the PDF button for shareable reports and print-friendly output.