How to Remember SOHCAHTOA (and Actually Use It)

6 min read · FlashDeck

The easiest way to remember SOHCAHTOA is to say it out loud as one silly word ("so-ca-toe-uh") and know what each chunk means: SOH = Sine is Opposite over Hypotenuse, CAH = Cosine is Adjacent over Hypotenuse, TOA = Tangent is Opposite over Adjacent. That's how to remember SOHCAHTOA. But remembering it is only half the job; you also need to pick the right ratio fast, which is what most of this post is about.

If SOHCAHTOA keeps vanishing right when the test starts, FlashDeck turns your trig notes into flashcards and brings them back right before you'd forget: Build my study plan.

What SOHCAHTOA means

SOHCAHTOA is a memory trick for the three basic trig ratios in a right-angled triangle (a right triangle, in US terms).

First, name the sides relative to the angle you care about (call it θ):

• Hypotenuse (H): the longest side, opposite the right angle. Always the same.
• Opposite (O): the side across from θ.
• Adjacent (A): the side next to θ that isn't the hypotenuse.

Then the ratios:

That's the whole SOHCAHTOA meaning. It's a key tool in GCSE maths (UK), grade 10 math (Canada) and US geometry and trig classes.

Mnemonics that stick

Some people remember the word itself. Others need a sentence. Try a few and keep the one that makes you laugh, because funny is what sticks.

Easy ways to remember SOHCAHTOA

• Say it like a word: "Soh-cah-toa." Some teachers pitch it as a made-up place name. Weird enough to remember.
• Some Old Horses Can Always Hear Their Owners Approach. Classic, clean, works.
• Silly Old Harry Caught A Herring Trawling Off America. Another long-time classroom favorite.
• Make your own: a sentence about your friends, your teacher, your group chat. Personal = memorable.

How to remember SOHCAHTOA: funny and rude versions

Yes, rude versions exist, and they get passed around every maths class and Reddit thread. They work for the same reason funny ones do: your brain remembers things that make you react. Keep it to your own notes and group chat, not your exam paper.

Write it, don't just read it

The best way to memorize SOHCAHTOA is to write it out from memory at the top of every trig worksheet for a week. After that, it's automatic.

Picking the right ratio (sin, cos or tan?)

This is where people actually lose marks. They know SOHCAHTOA but freeze on which one to use.

Use this three-step check every time:

1. Label the sides O, A, H from the angle's point of view.
2. Circle the two sides involved: the one you know and the one you need (or both you know, if finding an angle).
3. Find the chunk with both letters.
   • O and H → SOH (sin)
   • A and H → CAH (cos)
   • O and A → TOA (tan)

That's it. No guessing.

When to use sin, cos or tan: quick table

Worked examples

Example 1: finding a side with sin

A right triangle has hypotenuse 10 cm and angle 30°. Find the side opposite the angle.

• Have H, want O → SOH.
• sin 30° = O / 10
• O = 10 × sin 30° = 10 × 0.5 = 5 cm

Example 2: finding a side with tan

Angle 40°, adjacent side 8 m. Find the opposite side.

• Have A, want O → TOA.
• tan 40° = O / 8
• O = 8 × tan 40° ≈ 8 × 0.839 = 6.71 m (to 3 s.f.)

Example 3: finding an angle

Opposite side 5, hypotenuse 13. Find the angle.

• O and H → SOH.
• sin θ = 5 / 13
• θ = sin⁻¹(5 / 13) ≈ 22.6°

When you're finding an angle, use the inverse button (sin⁻¹, cos⁻¹, tan⁻¹), usually Shift + sin on most calculators.

Flashcards to drill it

Remembering SOHCAHTOA once is easy. Remembering it three months later in a mock, plus the exact values, plus which side is which, is harder.

How to remember SOHCAHTOA values (exact trig values)

At GCSE Higher and in many trig classes you're expected to know these without a calculator:

Notice sin goes up as cos goes down, and sin 30° = cos 60°. Patterns help.

Cards worth making

• Front: "SOH means?" Back: sin = opposite ÷ hypotenuse.
• Front: "Have A and H. Which ratio?" Back: cos.
• Front: "sin 60°?" Back: √3/2.
• Front: "How do you find an angle from two sides?" Back: inverse trig, e.g. sin⁻¹.

Then quiz yourself until it's boring. The problem is keeping track of which ones you've got and which you keep fumbling.

FlashDeck does that tracking for you. Paste your trig notes or a worksheet's text and it writes one card per fact or formula, using only what you pasted. Each day it shows only the cards you're about to forget, about ten minutes' worth. Missed sin 60°? It's back tomorrow. Knew it? It waits a day, then three, then longer. Build my study plan

For the rest of the formulas you need, see our best way to revise for maths GCSE, and if you're doing IB Math, how to study for IB exams.

Common mistakes

• Labeling sides from the wrong angle. Opposite and adjacent swap if you switch angles. Always label from θ.
• Calculator in radians. Check for a "D" or "DEG" on the screen. Radians give totally wrong answers.
• Dividing the wrong way. If x is on the bottom (like sin 30° = 5 / x), rearrange: x = 5 ÷ sin 30°.
• Using SOHCAHTOA on non-right triangles. It only works with a right angle. Otherwise you need the sine or cosine rule.
• Forgetting inverse for angles. sin θ = 0.5 doesn't mean θ = 0.5. Use sin⁻¹.

Remember SOHCAHTOA long after the test

Now you know how to remember SOHCAHTOA and how to use it; the last step is keeping it fresh. Paste your trig notes into FlashDeck, get a card for every ratio and exact value, and spend about ten minutes a day on only the ones you're about to forget.

Build my study plan

FAQ

What is an easy way to remember SOHCAHTOA?

Say it out loud as one word and break it into SOH, CAH, TOA. If that doesn't stick, use a sentence like "Some Old Horses Can Always Hear Their Owners Approach," or make up your own.

What does SOHCAHTOA stand for?

Sine = Opposite over Hypotenuse, Cosine = Adjacent over Hypotenuse, Tangent = Opposite over Adjacent. It's a mnemonic for the three trig ratios in a right-angled triangle.

How do I know when to use sin, cos or tan?

Label the sides from your angle, circle the two sides you have or need, and pick the chunk of SOHCAHTOA with both letters. O and H means sin, A and H means cos, O and A means tan.

How do you remember SOHCAHTOA exact values?

Learn the table for 0°, 30°, 45°, 60° and 90°, and notice the patterns (sin 30° = cos 60°, tan 45° = 1). Flashcards reviewed over several days work far better than reading the table once.

Does SOHCAHTOA work on any triangle?

No, only right-angled triangles. For other triangles, use the sine rule or cosine rule.