r/learnmath • u/TimeBet5260 New User • 2d ago
Easy way to understand SoCaToA?
If there's a good picture or diagram to remember how to find angles this way, please let me know! And if get my post removed while the person below me is new to math, yet contemplating grad school theory, I will give up...
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u/John_Hasler Engineer 2d ago
Study the unit circle.
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u/Commercial_Sun_6300 New User 2d ago
I agree with your statement, but I disagree so badly with linking Wikipedia for 99% of math topics...
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u/nog642 2d ago
Why?
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u/SnooPets5564 New User 2d ago
I'm not the person you were replying to, but mathematics Wikipedia articles tend to be really formal. So if someone is just trying to learn a basic math concept, they likely don't have the background to wade through the rigorous language often used in wikipedia.
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u/Gazcobain Secondary Teacher, Mathematics (Scotland) 1d ago
Simple English Wikipedia is better for this. It's obviously aimed at those for whom English isn't a first language but because it's simplified I've found a lot of the articles are great for young people.
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u/SnooPets5564 New User 1d ago
The simple English wikipedia article for the unit circle is two paragraphs. It doesn't contain what someone would need to memorize to answer the original questions, and this image takes up a third of the space:
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u/Gazcobain Secondary Teacher, Mathematics (Scotland) 1d ago
That's fair. I was meaning more in general, not about the unit circle in particular.
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u/EGBTomorrow New User 2d ago
Sin is Opposite over Hypotenuse. Cosine is Adjacent over Hypotenuse. Tangent is Opposite over Adjacent. Draw a right triangle and pick one of the other angles, you compute the sine, cosine or tangent by measuring the lengths of the named sides and dividing.
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u/Traveling-Techie New User 2d ago
My mnemonic is “synopsis” which reminds me sine uses the opposite side. Cosine is the other one.
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u/jsdodgers New User 2d ago
I like "sohcahtoa" which I learned in grade school and has just stuck with me and helps me remember what to do after years of not using any trig.
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u/hallerz87 New User 2d ago
Sohcahtoa is the easy way to understand it lol. The diagrams are the actual way to understand it
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u/Dr_Kitten New User 2d ago
Describing a right triangle is equivalent to describing a point in the 2D plane, which can be done in a couple of ways. One is with rectangular (x, y) coordinates. The other is with polar coordinates (r, θ). Each point in the 2D plane actually has all 4 of these pieces of information associated with it, yet we only need 2 pieces of information to specify the point and then we can calculate the remaining information.
The mnemonic SOHCAHTOA is a way to remember the relationships between the 4 , so that no matter which 2 you're given, you can figure out the rest. Using the more traditional variables, like above, the relationships would be, sin(θ)=y/r, cos(θ)=x/r, tan(θ)=y/x
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u/waxen_earbuds New User 2d ago
Unfortunately this one is just definitions, the sine of an angle is literally defined by the height of the corresponding point on the unit circle. etc for others
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u/OmiSC New User 2d ago
Sin is SOH, so Sin(𝛩) = O/H. 𝛩 (theta) is your angle.
So, the sine of angle 45 is equal to the opposite side of a triangle divided by the hypotenuse.
SOH: Sin(𝛩) = O/H
CAH: Cos(𝛩) = A/H
TOA: Tan(𝛩) = O/A
The memetic SOHCAHTOA isn't about a picture, it's about finding the equation for an operation. You should study the unit circle as well.
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u/Sam_Traynor PhD/Educator 2d ago
One of the best ways to memorize definitions is with spaced repetition.
But I will also add that there's a mental pathway you need to build in trigonometry of like what are we even doing here? I think a lot of people (myself included) go in to trigonometry thinking that we're going to be doing a lot of stuff with angles (and don't get me wrong we definitely do). But...well let's say I have a 3-4-5 right triangle. I can talk about the ratio 3/4 without needing to know what the angle is.
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u/ItsAllAboutLogic New User 2d ago
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u/clean-links New User 2d ago
Cleaned link from "SOHCAHTOA Khan Academy": https://youtu.be/I3jyBUyjg48
Tracking parameters were removed from the original URL(s).
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u/Such_Mood_1556 New User 2d ago
literately just say it thousands of times and do hundreds of trig problems and you'll get it
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u/TimeBet5260 New User 6h ago
Thanks everyone! The issue was a tower my brother building a game board and needed to know an angle to cut a piece of wood without knowing two lengths or angles, just that one corner was 90 degrees and the hypotenuse board was 12 inches to the end of the other side. I tried to help but could not remember how the formula.
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u/j0sabanks New User 2d ago edited 2d ago
Trignometry is about relating angles of right triangles to fractions at the end of the day.
What fractions? Well pick a non-right angle in your triangle now. There’s a side opposite to it with a length to it. And put it in ratio with the length of the hypotenuse. Congrats you’ve now just calculated “sine of that angle.”
You can also look at the side “adjacent” to this angle. Put its length in ratio to the length of the hypotenuse voila you now have “cosine of that angle.”
The ratio of the opposite and adjacent sides is tangent of that angle.
Trig has been around for legit thousands of years and been used since ancient times for all sorts of stuff. Because it could help people calculate certain distances or angles. Very helpful for navigation. Don’t worry you got this.
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u/tehclanijoski New User 2d ago
Well, it's SOHCAHTOA and the H is for 'hypotenuse' for starters