Deriving the formula for angle between two straight lines

[@mreverything7056]

Get yourselves a girl who looks at you the same way Prime Newtons looks at his camera when there's an earthquake XD

[@PrimeNewtons]

🤣🤣🤣🤣🤣🤣🤣🤣

[@creativename.]

😂

[@lornacy]

And thanks the Lord.

[@johnroberts7529]

Your lessons are so beautifully constructed and delivered. Great stuff! Please keep making them. 😊

[@PrimeNewtons]

Thank you! Will do!

[@johnroberts7529]

You're very welcome.

[@kragiharp]

Yes, very enthusiastic about math and very motivating. 👍 ❤️🙏

[@Orillians]

Some day I gotta meet you and thank for you for inpsiring my mathematical passion!!!!!

[@PrimeNewtons]

Maybe one day!

[@stvp68]

Your chalkboard handwriting is so pretty. I wish mine was that nice!

[@JSSTyger]

Its called a math quake. It happens when chalk rubs harshly against the chalkboard when one gets too excited about doing math.

[@Jason-ot6jv]

I always liked this formula because if you look at it and try things like: Limit as m1m2 approach -1, you will get 90 degrees which makes sense since one of the rules for perpendicularl lines is that m1m2 = -1. Also you can do a similar observation when m1 = m2 (parallel lines since same slope) you will get arctan(0) or 0, which also makes sense since the lines are parallel.

[@AQIMGame]

i was just trying to derive the formula and this video came up couple of minutes later, though ur proof is easier to understand😂

[@hvok99]

Ha, loved the cold open. Great video.

[@jamal369]

You are so good at teaching. Keep it up!

[@PrimeNewtons]

Thank you! 😃

[@jamal369]

no problem@@PrimeNewtons

[@chorobatestopografia7689]

gracias, por tu clara explicación paso a paso

[@ena6631]

You are very good. Funny too and expressions entice your students. Well done, more please.

[@PrimeNewtons]

Thank you! 😃

[@Toto-cm5ux]

It's very smart and interesting! However, does it work when beta is equal to pi over two? Moreover, I wonder how to justify to put the absolute value on the fraction.

[@josephbaker9932]

Would it work to take the arctan(m1) = alpha and the arctan(m2) = gamma, then gamma - alpha = beta?

[@moseschandiga8496]

Enjoyed it very well, thanks dear!

[@henryubah5031]

The man does love his cap.

[@lethalsub]

I was waiting for you to say "...take the magnitude of the earthquake, er tangent...".

[@lukaskamin755]

Very interesting, never happened to see this formula inferred

[@m.h.6470]

Solution: Since m describes the slope (m > 0) or dip (m < 0) per unit of x of the respective line, you can easily calculate the angle between that line and the x-axis with tan⁻¹(|m|). So the angle between two lines is: (with m₁ ≥ m₂) if m₁, m₂ > 0 then tan⁻¹(m₁) - tan⁻¹(m₂) if m₁ > 0 > m₂ then tan⁻¹(m₁) + tan⁻¹(-m₂) if 0 > m₁, m₂ then tan⁻¹(-m₂) - tan⁻¹(-m₁)

[@m.h.6470]

The video only shows the solution for m₁, m₂ > 0 😕

[@budderzmonahan6215]

Would it not be simpler to say that alpha and gamma = arctan of m1 and m2, and beta = gamma -alpha, so beta = arctan m2 - arctan m1? Or is my reasoning flawed?

[@aubrey1008]

When these lines are translated to the origin, doesn't b1 and b2 both equal zero?

[@ahmedabdelkoui3790]

The two parallel lines to the first and passing through the origin have their respective equations: y=mx and y=m'x (y-intercept zero).

[@surendrakverma555]

Thanks 🙏

[@jadenredd]

God wanted to make sure you know that we don’t live under Euclidean geometry 😂😂

[@-wx-78-]

Orthogonal lines have m₂ = -1/m₁, hence denominator is zero, so we have arctangent of infinity/undefined. 😉 Line y = m₁x+b₁ is collinear with vector r₁=(1; m₁), second one - with r₂=(1; m₂). Scalar product (r₁, r₂) = 1+m₁m₂ = |r₁||r₂|cos Θ ⇒ cos Θ = (1+m₁m₂)/(√[1²+m₁²]√[1²+m₂²]) ⇒ Θ = arccos((1+m₁m₂)/√[(1+m₁²)(1+m₂²)].

[@chorobatestopografia7689]

asombroso Θ = arccos((1+m₁m₂)/√[(1+m₁²)(1+m₂²)].

[@JAMESYUN-e3t]

Excellent

[@BartBuzz]

Curious why you didn't just move the x-y coordinates to where the two lines intersect and call the transformed coordinates x'-y''? That would eliminate having to draw the added parallel lines. The proof would be the same. I'm assuming you thought a coordinate transformation would confuse some of your viewers?

[@PrimeNewtons]

Oh yeah! I was imagining 9th graders

[@BartBuzz]

@@PrimeNewtons There are some smart 9th graders if they have understood your Lambert W videos 😉

[@loveyouself5389]

Wow, aweome man !

[@andrejflieger4182]

Hmm, didn't you record exactly the same thing just a few days ago, did you?

[@PrimeNewtons]

This is to derive the formula

[@achievemindset9513]

thank you

[@BhavaySharma-co2rg]

11th std. Student ❤ From india❣️

[@qwertyuiop2161]

Reminds me of problem 11 on AMC12A 2023

[@rssl5500]

Nice video :)

[@dinabandhusaha5520]

❤

[@0llie]

no way an earthquake 😭 what are the chances of recording that

[@PrimeNewtons]

I was hoping to see the shaking in the video, but optical stabilization in the camera ruined it 😢

[@sammascreel]

@@PrimeNewtons I did hear it

[@lornacy]

One. The chance was one. 😂 (Someone had to say it)

[@holyshit922]

Forgot mention what happens when denominator is zero

[@JourneyThroughMath]

Id say the spherical earth got jealous of the flat plane

[@klementhajrullaj1222]

Never stop earthquake! 😂😀😉

[@noertri618]

I love geometry

[@albertofernandez6861]

y1=m1x+b1 y2=m2x+b2 y1'=m1=tan(alfa) y2'=m2=tan(alfa+beta) tan(alfa+beta)=(tan(alfa)+tan(beta)/(1-tan(alfa)•tan(beta) m2=(m1+tan(beta))/(1-m1•tan(beta) m2(1-m1•tan(beta)=m1+tan(beta) m2-m1•m2•tan(beta)=m1+tan(beta) tan(beta)+m1•m2•tan(beta)=m1-m2 tan(beta)(1+m1•m2)=m1-m2 tan(beta)=(m1-m2)/(1+m1•m2) beta=arcotan(m1-m2)/(1+m1•m2)

[@축복이-x6u]

asnwer=2 isit hmm gmm

[@junkgum]

Them fault lines though

[@PrimeNewtons]

Scary

[@wintape]

qaqas bu ne emosiyadi verirsen zemlyatresenyaya gore da noooldu