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Sohcahtoa Calculator Degrees

Reviewed by Calculator Editorial Team

This SOHCAHTOA calculator helps you find sine, cosine, and tangent values for angles measured in degrees. Whether you're studying geometry, physics, or engineering, this tool provides quick and accurate trigonometric calculations.

What is SOHCAHTOA?

SOHCAHTOA is a mnemonic device used to remember the three primary trigonometric functions: sine, cosine, and tangent. Each letter stands for a ratio that relates the sides of a right-angled triangle to one of its angles.

SOH - Sine = Opposite / Hypotenuse

CAH - Cosine = Adjacent / Hypotenuse

TOA - Tangent = Opposite / Adjacent

This calculator uses these relationships to compute trigonometric values when you provide the angle in degrees and the lengths of the triangle sides.

How to Use This Calculator

  1. Enter the angle in degrees (0° to 360°)
  2. Input the length of the opposite side (if known)
  3. Input the length of the adjacent side (if known)
  4. Click "Calculate" to see the results
  5. Use the "Reset" button to clear all inputs

For angles between 0° and 90°, all sides are positive. For angles between 90° and 180°, the opposite side becomes negative. For angles between 180° and 270°, both opposite and adjacent sides are negative. For angles between 270° and 360°, the adjacent side becomes negative.

Formula Explained

The calculator uses the following formulas based on the SOHCAHTOA mnemonic:

Sine (sin) = Opposite / Hypotenuse

Cosine (cos) = Adjacent / Hypotenuse

Tangent (tan) = Opposite / Adjacent

Where:

  • Opposite - The side opposite to the angle
  • Adjacent - The side adjacent to the angle
  • Hypotenuse - The longest side of the right-angled triangle

The calculator first calculates the hypotenuse using the Pythagorean theorem if both opposite and adjacent sides are provided.

Worked Example

Let's calculate the trigonometric values for a 30° angle with opposite side = 1 and adjacent side = √3.

  1. Calculate hypotenuse: √(1² + (√3)²) = √(1 + 3) = 2
  2. Sine (sin) = Opposite / Hypotenuse = 1 / 2 = 0.5
  3. Cosine (cos) = Adjacent / Hypotenuse = √3 / 2 ≈ 0.866
  4. Tangent (tan) = Opposite / Adjacent = 1 / √3 ≈ 0.577

These values match the known trigonometric values for 30°.

Frequently Asked Questions

What is the difference between degrees and radians?
Degrees are a unit of angle measurement where a full circle is 360°. Radians measure angles based on the radius of a circle, with π radians equal to 180°. This calculator uses degrees.
Can I use this calculator for non-right-angled triangles?
No, this calculator is specifically designed for right-angled triangles where one angle is exactly 90°. For other triangles, you would need a different approach.
What if I only know one side and an angle?
You can use the inverse trigonometric functions (arcsin, arccos, arctan) for this scenario, but this calculator requires both sides or the hypotenuse to be known.
How accurate are the results?
The results are accurate to 10 decimal places, which is sufficient for most practical applications. The calculator uses JavaScript's built-in Math functions.