You're staring at a grid. It’s Friday, or maybe a particularly mean Tuesday, and the clue just says "Trig ratio." Four letters. Or maybe three. Or five. Your brain freezes because, honestly, who actually remembers 10th-grade geometry when they’re just trying to enjoy a coffee and a puzzle?
Crossword constructors love trigonometry. It’s a goldmine of short, vowel-heavy words that help them escape the "corner of death" where nothing else fits. But for the solver, it can be a bit of a nightmare if you don't have the shortlist of usual suspects memorized. Most people assume there are only three options—Sine, Cosine, and Tangent—but the New York Times and LA Times crosswords frequently dig deeper into the mathematical bargain bin.
The Usual Suspects: Most Likely Answers for a Trig Ratio Crossword Clue
If you see a three-letter space, you're almost certainly looking for SIN, COS, or TAN. These are the abbreviations for the "big three" ratios. In the world of the New York Times crossword, edited by Will Shortz (and now overseen by a dedicated team), SIN is the most frequent flier. It’s three letters, it starts with a common consonant, and it ends with a very useful 'N'.
But wait.
What if the grid asks for four letters? That’s where things get slightly more annoying. You might be looking for SINE. It’s the full name. It’s elegant. It’s also a frequent answer because of that terminal 'E', which is the most common letter in the English language and a godsend for connecting horizontal and vertical words.
Then we have the five-letter heavyweights. COSIN is rarely used in its abbreviated five-letter form; usually, constructors go for the full COSINE. If it’s seven letters? TANGENT. But let’s be real, seven-letter slots are usually reserved for more interesting words than math terms unless the puzzle has a specific STEM theme.
When the Clue Gets Tricky: Beyond the Basics
Sometimes a constructor wants to be a bit "clever." They won't just say "Trig ratio." They’ll say "Ratio of opposite to hypotenuse."
That’s SINE.
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Or "Ratio of adjacent to hypotenuse."
That’s COSINE.
If you remember the old mnemonic SOH CAH TOA, you’re ahead of the game. Sine = Opposite / Hypotenuse. Cosine = Adjacent / Hypotenuse. Tangent = Opposite / Adjacent. It’s a bit of a mouthful, but in the heat of a crossword battle, reciting that old school chant can save you from a DNF (Did Not Finish).
There are also the "reciprocal" ratios. These are the ones that really make people groan. If you see a six-letter slot and the clue is "Trig ratio," you might be looking at SECANT. It’s the reciprocal of the cosine. Then there’s COSEC (short for cosecant) or COTAN (short for cotangent). These are the deep cuts. They don't appear often, but when they do, they’re usually there to help the constructor navigate a particularly difficult cluster of letters.
Why Crossword Constructors Obsess Over Trig
Crosswords are built on a foundation of "crosswordese"—words that you rarely use in real life but are essential for filling a 15x15 grid. Trig ratios are the ultimate utility players.
Think about the letters in SINE. S, I, N, and E are all high-frequency letters. They’re like the bricks in a sturdy wall. If a constructor has a word like RELINE going vertically, and they need a horizontal word that starts with 'I' and ends with 'N', SIN is a perfect candidate. It’s efficient. It’s clean.
Actually, the word SECANT is a favorite for Saturday puzzles. It’s just obscure enough to trip up a casual solver but familiar enough to anyone who didn't sleep through high school math. It provides a nice 'C' and 'T', which are great for branching out into longer, more complex words like CATNIP or STANCE.
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Real Examples from Famous Puzzles
Let’s look at some historical data. In the NYT Crossword, the clue "Trig ratio" has appeared hundreds of times.
- SIN: Often clued simply as "Trig ratio" or "Math ratio."
- COS: Sometimes clued as "Trig function" or "Neighbor of tan."
- TAN: Frequently clued with a pun, like "Beach shade?" or "Sun-related trig ratio?" (Constructors love a bad pun).
- COT: While it usually refers to a small bed, in a math-heavy puzzle, don’t rule out "Cotangent" abbreviation.
There was a puzzle back in 2014 where the clue was "Trig ratio involving the hypotenuse." That’s a bit mean because it could be either SINE or COSINE. In that case, you have to look at the "crosses"—the words intersecting it—to figure out if the first letter is an 'S' or a 'C'. This is where the strategy of "pencil it in" comes in handy.
The Geometry of the Grid
Math in crosswords isn't just limited to the ratios themselves. Sometimes the clue is "Trig. topic," and the answer is ANG (short for angle) or TRI (short for triangle).
If you’re stuck on a "Trig ratio" clue, check the neighboring words. If you see a lot of 'Z's, 'Q's, or 'X's nearby, the constructor might be using one of the weirder ratios to make the grid work. But 90% of the time, it's going to be one of the big three.
Interestingly, the word ARCSIN or ARCCOS occasionally pops up in larger Sunday puzzles (21x21 grids). These are the inverse functions. They are long, they are clunky, and they are usually the sign of a constructor who is either very proud of their math degree or very desperate to fill a seven-letter gap.
Common Pitfalls and How to Avoid Them
The biggest mistake people make? Overthinking it.
They see "Trig ratio" and they immediately start trying to remember the unit circle or the Pythagorean theorem. Don't do that. Treat it like a vocabulary test, not a math test.
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Check the letter count first.
- 3 letters: SIN, COS, TAN.
- 4 letters: SINE.
- 5 letters: COSIN (rare), COTAN (rare).
- 6 letters: COSINE, SECANT.
Another thing to watch for is the "abbreviation flag." If the clue has a period at the end, like "Trig. ratio," it’s a dead giveaway that the answer is an abbreviation like SIN or COS. If there’s no period, it’s a toss-up, but usually, the full word is preferred for longer slots.
How to Solve the "Trig Ratio" Clue Every Time
Keep a mental "math cheat sheet" when you solve.
Crosswords are about patterns. If you see "Trig" in the clue, your brain should immediately toggle into a specific mode. You aren't looking for "Ratio" in a general sense (like "rate" or "odds"). You are looking for these specific six or seven words.
If you're really stuck, look for the 'S' or the 'T'. Most trig words start with one of those two. If the second letter is an 'I', it’s SIN. If it’s an 'E', it’s SECANT. If it’s an 'A', it’s TAN.
Crosswords are supposed to be fun, but math clues can feel like a pop quiz you didn't study for. Just remember that the constructor is probably using that word because they had no other choice. They aren't trying to test your knowledge of trigonometry; they’re trying to find a way to connect OBOE to ERASED.
Next time you see it, don't panic. Count the boxes, look for the 'N' or the 'E' at the end, and slot it in. You've got this.
Actionable Insights for Crossword Success
- Memorize the "Big Three" abbreviations: SIN, COS, TAN are your most frequent three-letter answers.
- Watch for the abbreviation signal: A period in the clue (Trig. ratio) almost always means a three-letter abbreviation is coming.
- Use the terminal letter: Crossword trig answers often end in E (SINE, COSINE) or N (SIN, TAN), which are excellent for checking your intersecting vertical clues.
- Don't forget the reciprocals: For 6-letter slots, SECANT is the most common answer that isn't COSINE.
- SOH CAH TOA is your friend: If the clue is specific about "opposite" or "adjacent" sides, use the mnemonic to identify if it's SINE, COSINE, or TANGENT.
The most effective way to master these clues is through exposure. Keep a list of "crosswordese" math terms in your notes app. When you encounter a weird one like ARCTAN or COSEC, jot it down. Over time, your brain will stop seeing "math" and start seeing "filler," which is exactly how a pro solver handles it.
Start by looking at the intersections. If you have a 'T' as the first letter and a three-letter space, just put in TAN. If it doesn't work, erase it and try SIN. Crosswords are a game of trial and error, and trig ratios are the perfect place to practice that. No calculator required.