Trig Degree Calculator

How to use the Trig Degree Calculator

What this calculator does

This calculator evaluates sine, cosine, tangent, cotangent, secant, and cosecant for one real angle. It accepts either degrees or radians, converts the input to a canonical radian measure, and then reports dimensionless function values. It is useful for checking unit-circle exercises, preparing geometry or physics work, validating spreadsheet formulas, and comparing reciprocal identities. It does not solve a triangle from side lengths, choose the correct branch of an inverse trigonometric function, or prove an identity. For the geometric foundation, see OpenStax's explanation of the unit circle definitions of sine and cosine.

When to use it

Use the calculator when you need all six functions for a known angle, when you want to check whether a reciprocal function is undefined, when you are converting a degree-based problem to radians, or when you need a clean workbook containing the current input and results. It is especially helpful around special angles such as 0°, 30°, 45°, 60°, and 90°, where exact identities make mistakes easy to spot.

How to calculate

1. The calculator opens with a ready-to-use demonstration: Angle = 30 and Angle unit = Degrees. The displayed results and the example XLSX workbook are available immediately.
2. Replace the number in Angle with a standard decimal. The result updates live. Do not use grouping commas, decimal commas, scientific notation, or a unit symbol inside the field.
3. Choose Degrees or Radians under Angle unit. When you switch units, a valid current value is converted so the represented angle stays the same.
4. Read the six result cards and the Function detail table. “Undefined” means the relevant identity divides by zero; it is not the same as a very large finite answer.
5. Select Download Excel to export the current validated model as a real XLSX workbook. Reset clears the demonstration data, removes calculated content, and disables export until you enter a complete valid angle again.

Input guide

Angle is required. Enter one finite decimal between – 1,000,000,000 and 1,000,000,000 in the active unit; examples include 30, – 45.5, or 0.5235987756. A higher or lower value rotates around the unit circle, so the outputs change periodically rather than monotonically. A common mistake is entering “30°” or “1,5”: symbols and decimal commas are rejected instead of being silently reinterpreted.

Angle unit is required and offers Degrees or Radians. Degrees measure one full revolution as 360°, while radians measure it as 2π. Selecting Radians converts a valid 30° input to approximately 0.5235987756 rad. A common mistake is entering a radian value while Degrees remains selected, which evaluates a completely different angle. LibreTexts provides a concise reference for converting between degrees and radians.

Output guide

Degrees and Radians show the same input angle in both systems. Quadrant reports I, II, III, IV, or Axis after normalizing the angle to one revolution; this helps interpret signs but is not a separate trigonometric result. Sine and Cosine are the unit-circle y- and x-coordinates. Tangent is sine divided by cosine, and Cotangent is cosine divided by sine. Secant and Cosecant are the reciprocals of cosine and sine. Zero is a valid result for sine, cosine, or tangent where defined. A reciprocal or quotient becomes undefined only when its denominator is zero. OpenStax's discussion of tangent, cotangent, secant, and cosecant explains these relationships in unit-circle terms.

Worked example

With the startup values, θ = 30° = π/6 ≈ 0.5235987756 rad. The calculator obtains sin(30°) = 0.5 and cos(30°) ≈ 0.8660254038. It then computes tan = 0.5 ÷ 0.8660254038 ≈ 0.5773502692, cot ≈ 1.7320508076, sec ≈ 1.1547005384, and csc = 2. These values match the first-open cards, detail table, and workbook checkpoints.