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How to Put Sohcahtoa in Calculator

Reviewed by Calculator Editorial Team

SOHCAHTOA is a mnemonic device used to remember the three primary trigonometric ratios in right triangles: sine, cosine, and tangent. This guide explains how to properly apply SOHCAHTOA in a calculator for accurate trigonometric calculations.

What is SOHCAHTOA?

SOHCAHTOA is an acronym that stands for:

  • Sine = Opposite / Hypotenuse
  • Opposite
  • Hypotenuse
  • Cosine = Adjacent / Hypotenuse
  • Adjacent
  • Tangent = Opposite / Adjacent
  • Opposite
  • Adjacent

This mnemonic helps students remember which sides of a right triangle correspond to each trigonometric function. The letters SOH and CAH represent the sine and cosine ratios, while TOA represents the tangent ratio.

How to Use SOHCAHTOA

To use SOHCAHTOA in a calculator, follow these steps:

  1. Identify the sides of the right triangle: opposite, adjacent, and hypotenuse.
  2. Determine which trigonometric function you need to calculate (sine, cosine, or tangent).
  3. Use the appropriate ratio from SOHCAHTOA to set up the calculation.
  4. Enter the values into your calculator and perform the division.
  5. Interpret the result based on the units of the sides.

Remember that the hypotenuse is always the side opposite the right angle and is the longest side of the triangle. The opposite side is opposite the angle you're interested in, and the adjacent side is next to that angle.

Calculator Method

When using a calculator with SOHCAHTOA, you'll typically:

  1. Enter the length of the known sides
  2. Divide the appropriate sides based on the function you need
  3. Calculate the result
  4. Convert to degrees if needed (most calculators use radians by default)

Sine Formula: sin(θ) = opposite / hypotenuse

Cosine Formula: cos(θ) = adjacent / hypotenuse

Tangent Formula: tan(θ) = opposite / adjacent

Example Calculation

Let's say you have a right triangle with:

  • Opposite side = 3 units
  • Adjacent side = 4 units
  • Hypotenuse = 5 units (since 3² + 4² = 5²)

To find the sine of angle θ:

  1. Identify that sine uses opposite/hypotenuse
  2. Set up the calculation: sin(θ) = 3/5
  3. Enter into calculator: 3 ÷ 5 = 0.6
  4. Convert to degrees if needed: arcsin(0.6) ≈ 36.87°

Most scientific calculators use radians by default. To convert to degrees, you may need to use the degree mode or multiply by 180/π.

Common Mistakes

When using SOHCAHTOA in a calculator, watch out for these common errors:

  • Mixing up the order of the sides (opposite vs. adjacent)
  • Forgetting to square the sides when calculating the hypotenuse
  • Using the wrong trigonometric function for the problem
  • Not converting between degrees and radians when needed
  • Rounding too early in the calculation process

FAQ

What does SOHCAHTOA stand for?

SOHCAHTOA stands for Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, and Tangent = Opposite/Adjacent. It's a mnemonic device to help remember the three primary trigonometric ratios.

When should I use sine, cosine, or tangent?

Use sine when you know the opposite side and hypotenuse, cosine when you know the adjacent side and hypotenuse, and tangent when you know both the opposite and adjacent sides.

How do I know which side is opposite or adjacent?

The side opposite the angle is across from it, and the adjacent side is next to the angle. The hypotenuse is always the longest side, opposite the right angle.

Can I use SOHCAHTOA with non-right triangles?

No, SOHCAHTOA only applies to right triangles. For non-right triangles, you would need to use the Law of Sines or Law of Cosines.

How do I convert between degrees and radians?

To convert degrees to radians, multiply by π/180. To convert radians to degrees, multiply by 180/π. Most scientific calculators have a degree/radian mode switch.