Deriving the formula for angle between two straight lines

In this video , I showed how to obtain the formula for the angle between two lines using the slopes

[mreverything]

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

[johnroberts]

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

[Orillians]

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

[Jason-otjv]

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.

[JSSTyger]

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

[stvp]

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

[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😂

[jamal]

You are so good at teaching. Keep it up!

[ena]

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

[hvok]

Ha, loved the cold open. Great video.

[chorobatestopografia]

gracias, por tu clara explicación paso a paso

[lukaskamin]

Very interesting, never happened to see this formula inferred

[m.h.]

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)

[jadenredd]

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

[-wx--]

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 =

[ahmedabdelkoui]

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).

[lethalsub]

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

[Toto-cmux]

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.

[llie]

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

[josephbaker]

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