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I’m pretty dumb, so I don’t understand this one.
Pythagorean theorem.
Although, don’t solve this or else Pythagoras might throw you off of a boat
Pretty sure this is Pythagorean Identity, theorem is a²+b²=c²
Probably that trigonometry is the highest math the average person will take?
I got to calculus 2 and proceeded to forget everything through algebra II once I took a break from math for a semester.
You leave my unit circle alone!
Why?
SOH CAH TOA
Ah, sohcahtoa. Not to be confused with
Thx, this is not helpful, but I will never be able to think of it any other way now
Please elaborate.
Sine of theta is the ratio of the lengths of the Opposite side over the Hypotenuse (SOH). Cosine of theta is Adjacent over Hypotenuse (CAH). Tangent of theta is Opposite over Adjacent (TOA).
Oh you’re saying opposite site and adjacent site in English
Anyway how is the r=1 circle harmful for that?
It’s not. It’s just one of those things that people groan about because when you first learn it the concept is confusing. After about 15 minutes of instruction on a unit circle, it’s not a big deal at all.
How do you know which one is “opposite” and adjacent? They could literally be exactly the same but in any case they both touch the hypotenuse?
Adjacent or opposite to the angle you’re referring to.
So the picture is wrong then, the marked angle is top right (and the right angle, of course), the other angle is not marked, so adjacent and opposite are swapped.
The one with the Jedi? Yes, was wondering about that too. If you get through the trouble creating something like that you should really try to make it right.
Believe this was featured in a paper that recently used trig to prove the Pythagorean theorem (previously thought to be a circular definition). I think some highschoolers cracked it as part of a mathematics challenge or something.
Someone needs to turn this into loss
Why is it 1
It was freely chosen for simplicity.
If you choose another R, the other sides (x and y) become R*cos(th) and R*sin(th)
I don’t understand what is harmful about the unity circle either.
Any circle could have its radius technically be 1, as long as you set the units of measurement so that 1 equals the radius of the circle.
units? what are those? I never use units, or pay attention to capitals. pure math ftw, baby!
spoiler
Rapidly hides from the science professors
Pure math uses units. Like they say “1 unit”
Sometimes the units are given cute names like “wiggly waggly units” to make physicists cringe. Acknowledging a unit with cute names when the unit is not important is entertaining.
Because it’s a unit circle.
for the same reason that rulers start with 1, it would be utterly pointless to use anything else.
Your ruler starts with 1? How do you measure stuff between 0 and 1?
those are unlabeled, have you ever seen a ruler?
I am fascinated, can you show a picture
Zero is not unlabelled lol
the unit circle lives in my nightmares.
Took me a minute to notice, but it was worth it
Notice what??
You can use the spoiler tag
No spoiler
Notice what, exactly. I still don’t get it.
Take a look again, it’s still there
I only see the double arrows.
When you look at it for a minute, your phone will dim the screen and in reflection you’ll see the person who has harmed you.
I’ve seen it! The bastard!
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SOH CAH TOA is just a trick to make rote memorization of procedure easier. Understanding the unit circle will let you understand what trigonometry is actually doing.
Yeah, dividing a circle into 360 parts, then subdividing those by 60, and further subdividing those by 60 makes so much more sense than just using ratio of a number fundamental to circles themselves.
