On an Unit circle:
Sine and Cosine build a right triangle with the radius which lenght is one. So sin²(θ)+cos²(θ)=1²=1
cerwe
I've been through three pre-calc/trig textbooks looking for a proof on the three main identities. Still hadn't seen it until I ran across this video. Thank you very much!
sloanbell
Fun fact: Pythagoras, the creator of the Pythagorean Theorem, was also a cult leader. One time he and his members were locked in a room and needed to get out. Pythagoras had his members form a human ladder to the window at the top, and he climbed out, leaving his members alone in the aforementioned room to die.
LuckyPigeon
You put 1+cot(theta)=cot(theta) in the description and scared the sh!t outta me lol
DarthSagit
While watching the last few minutes, I realized you can get an interesting relationship csc^2 (theta) + sec^2(theta) = 1/(sin^2(theta)•cos^2(theta) ) and then use the double angle formula sin(2•theta) = 2•sin(theta)•cos(theta) to get an expression for the inverse of sin^2(2•theta) or the inverse of that to be 1/(sec^2 + csc^2)
dougr.
4:30, Well Proved. Was very helpful to me.
shrey
I needed this video, thank you very much for making it❤
Salma-qyqb
i was struggling with this problem for hours, thank you!!!
HokageArtz
Consider the graph y = x
consider the distance from origin to the point some finite radius 'r'
let's say the angle it makes is ∆ (I know choosing ∆ as an angle is pretty weird but.. bruh my keyboard doesn't have many math symbols)
Now you know that sin∆ = y/r, cos∆ = x/r
=> x = rcos∆
y = rsin∆
Now using the Pythagorean theorem and plugging in for x and y
We get r²(sin²∆+cos²∆) = r²
Since r > 0 we can cancel it out, when r is 0, namely the distance from the origin is 0, or the side length for hypotenuse is not there, thus a right triangle can't be formed, we are talking about (x, y) € (0, 0), trivial...
So we get : sin²∆ + cos²∆ = 1
HappyAlien-cwko
You r such a life saver thank u so much
alissa
Is there any way to prove sin^2(θ)+cos^2(θ)=1 without using the Pythagorean theorem? I’m 13 and trying to prove the Pythagorean theorem. I’ve done it for where a=b, but I’m struggling to find an original one for where a≠b. Thanks a lot!
elord
Question: could we have proven this with a reference to the unit circle (i.e. c = 1)?
bullinmd
Tomorrow is my exam and I got the solution thankyou very much 🙏
ayushitripathi
It can be proved using similar triangles
holyshit
This is a stretch since it's been a year, but hopefully someone will answer: how does this prove for any angle theta? If we use right triangles then theta is strictly between 0 and 90 degrees, how is this proof valid for angles greater than 90?
duvni
Put a video about why sine is opposite over hypotenuse... Pls pls pls
logusathish
sin^2(theta)+cos^2(theta)=1 is known as the idiot formula in Denmark. i have no idea why.
klausolekristiansen
why should we divide C square on both sides
venugopal-tndg
You are as good as if not better than PatrickJMT. You're definitely better than Salmon Kahn.
millej
also, sin^2(2theta)+cos^2(2theta)=1 for the same reasons
