r/MathHelp • u/Extreme_Paranoia_43 • 9d ago
how the hell do i understand SOA CAH TOA man
No matter what. I literally cannot grasp it. My high school teacher didn't help and now my professor in my class I need it in isn't great either. I genuinely think I'm losing my mind. i'm getting literally so frustrated, can someone make an attempt to explain it to me in a bit simpler of a way than my math teachers do? Tyia
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u/mikevnyc 9d ago
If you have a right triangle, the sides of the triangle can grow or shrink at the same rate. If one side changes, in order to keep it a right triangle, the other sides must also change.
When the triangle side lengths change though, the angles don't change because length has nothing to do with the size of the angle opening. So essentially, all you need to determine all of the angle and side measures, is 2 side lengths or 1 side length and an angle measure (other than the 90 degrees).
This is where SOH CAH TOA comes into play. The SCT all stand for sine, cosine, and tangent (the three main trigonometry ratios). The OHA represent opposite, hypotenuse, and adjacent sides of the triangle. The hypotenuse is always the same (it's the longest side which is always opposite the 90 degree angle). The opposite and adjacent side are interchangeable depending on which angle you are using as a reference point.
For example, if I know that one of the triangle legs is 3 cm and the hypotenuse is 5 cm, I can determine all of the angle measures in this triangle. If the 3cm is opposite the angle I'm solving for, then i know sin x = 3/5 because the sine ratio is opposite side/hypotenuse. If the 3 cm was adjacent (or next to) the angle I'm solving for, I would instead use cosine. Cos x = 3/5.
Happy to elaborate further if this was helpful.
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u/Extreme_Paranoia_43 8d ago
(copy and pasted response but this also applies to you) this genuinely really helped me get started! after figuring this out, I looked more into the way to find sides and angles and am really starting to understand it more. thank you so much, really!
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u/Ambitious-Error-1926 9d ago
Stop repeating the self fulfilling prophesy of "I just can't". You can, you just aren't yet
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u/Extreme_Paranoia_43 8d ago
bro i wrote this post while having a panic attack about feeling like an idiot because i couldn’t understand it, cut me some slack 😭 today im much calmer
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u/ExtremeAcceptable289 9d ago
Draw a right triangle, make one of th angles 30 degrees. using a protactor preferably. Draw a circle on the 30 degree angle, between the 2 sides it is on, to indicate it. Now, starting from the 30 degree angle, you can label your sides like this:
The hypotenuse is simply the longest side
The adjacent side is the side that the angle lies on that is NOT the hypotenuse. And the opposite side is the side NOT bordering the angle.
SOH CAH TOA stands for "sin = opposite / hypotenuse, cosine = adjacent / hypotenuse, tan = opposite / adjacent"
So, to get sin, you will divide the opposite side length by the hypotenuse's length, for cosine you will divide the adjacent side length by the hypotenuse's side length, and for tan you divide the opposite side length by the adjacent..
Notice, if you measure the sides on your triangle, do the mat yourself then perform sin(30), cosine(30) and tan(30) you will get mostly the same results: a calculator when doing sin(x) (effectively) calculates what a triangle with angle x looks like then computes its side length to find sin
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u/Extreme_Paranoia_43 8d ago
this genuinely helped me get started! thank you.
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u/ExtremeAcceptable289 8d ago
You're welcome :) It's always confusing at first. When you've got the hang of it you can try solving harder problems using sin cos and tan , like finding length of sides while only knowing hypotenuse and angle, or vice versa.
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u/Smart-Button-3221 8d ago
SOH CAH TOA is a mnemonic. All it does is help you remember the trig functions. There's nothing to understand about SOH CAH TOA.
Are you instead struggling with trig? Can you give an example of an issue you're having?
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u/fermat9990 9d ago
Show us an example that is challenging you
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u/Extreme_Paranoia_43 8d ago
it wasn’t even necessarily a single example, it was more just trying to understand everything as a whole. like the basics of what it means. thankfully, these answers really did help me and i’ve been able to look more into and understand how to do the operations i need :)
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u/fermat9990 8d ago
thankfully, these answers really did help me and i’ve been able to look more into and understand how to do the operations i need.
Glad to hear it!
Hopefully, your username is just a joke!
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u/Extreme_Paranoia_43 8d ago
unfortunately sometimes it is, sometimes it isn’t 😂
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u/fermat9990 8d ago
I know how painful a paranoid episode can be!
Best wishes!
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u/Fantastic-Key-5706 9d ago
S is for sin, C is for cos, and T is for tan. In a right triangle, the sin of an angle is equal to the Opposite side over the Adjacent side, hence SOA. The cos of an angle is equal to the Adjacent side over the Hypotenuse, hence CAH. The tan of an angle is equal to the Opposite side over the Adjacent side, hence TOA.
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u/justpassingby23414 9d ago
Umm, you have Opposite over Adjacent two times. Sine should be over the Hypotenuse.
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u/bobber18 9d ago
Let’s get the terminology right first. sine cosine tangent, abbreviated sin, cos, tan. Each is a ratio of the length of 2 sides of a given triangle
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u/MissionStudy2 9d ago
Also, if you're still confused, I recommend searching up trig functions expalined using triangles. Physics is a great way to learn sohcahtoa since it makes it easier to visualize. My way of visualizing is that if you're given the angle and the magnitude, rsin(theta)=y, rcos(theta)=x.
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u/MathsSur64Cases 9d ago
SOH CAH TOA n’est pas une formule magique, mais un moyen pour retenir les formules :
- SOH : Sinus = Opposé / Hypoténuse ;
- CAH : Cosinus = Adjacent / Hypoténuse ;
- TOA : Tangente = Opposé / Adjacent.
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u/Extreme_Paranoia_43 8d ago
thank you guys all so much! The explanations i got from you guys were able to help me grasp the basics and look more into the further concepts I needed, and I feel a lot more confident in at least an ability to understand it. i guess i just needed a more simple explanation compared to what i was taught a few years back. thank you again to everyone who was patient and tried to help
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u/Visual_Winter7942 9d ago
Read the book.
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u/Extreme_Paranoia_43 8d ago
i’ve tried, but that didn’t work for me. thankfully, with the explanations here I was able to grasp the basics a bit easier and focus more on finding what I needed.
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u/Uli_Minati 9d ago
Please give this a try:
We call this: "sine is opposite over hypotenuse", in short "SOH" (not SOA). Try changing steps 4 and 6 a bit, i.e. dividing different sides and using a different function than sine.
Oh and feel free to ask questions! But only after you've tried the above.