Trig Calculator with Degrees and Minutes

This trigonometric calculator handles degree-minute-second inputs for precise angle measurements. Calculate sine, cosine, tangent, and other trigonometric functions with accurate degree-minute-second values.

How to Use This Calculator

Enter your angle in degrees, minutes, and seconds. Select the trigonometric function you want to calculate. Click "Calculate" to see the result in both decimal and degree-minute-second formats.

Note: For angles greater than 360°, the calculator will automatically convert to the equivalent angle between 0° and 360°.

Trigonometric Formulas

The calculator uses standard trigonometric formulas for degree-minute-second inputs. First, convert the angle to decimal degrees:

Decimal Degrees Conversion:

Decimal Degrees = Degrees + (Minutes / 60) + (Seconds / 3600)

Then apply the selected trigonometric function:

Sine: sin(θ)

Cosine: cos(θ)

Tangent: tan(θ)

Cosecant: csc(θ) = 1/sin(θ)

Secant: sec(θ) = 1/cos(θ)

Cotangent: cot(θ) = 1/tan(θ)

Worked Examples

Example 1: Calculating sin(45°30'15")

Convert to decimal degrees: 45 + (30/60) + (15/3600) = 45.5041667°
Calculate sin(45.5041667°) ≈ 0.7098
Convert result to degree-minute-second: 0.7098 radians ≈ 40°47'30"

Example 2: Calculating tan(30°)

Decimal degrees: 30°
Calculate tan(30°) ≈ 0.5774
Convert result: 0.5774 radians ≈ 33°41'30"

Frequently Asked Questions

What is the difference between degrees, minutes, and seconds?

Degrees measure the full circle (360°), minutes divide each degree into 60 parts, and seconds divide each minute into 60 parts. This system provides more precise angle measurements than decimal degrees alone.

Can I calculate trigonometric functions for angles greater than 360°?

Yes, the calculator automatically converts angles to their equivalent between 0° and 360° using modulo 360°.

What are the limitations of this calculator?

The calculator provides accurate results for standard trigonometric functions. For very precise calculations, consider using specialized scientific calculators or programming languages with higher precision arithmetic.