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turkey pot pies (mander.xyz)
submitted 8 months ago by fossilesque@mander.xyz to c/science_memes@mander.xyz
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[-] ryannathans@aussie.zone 1 points 8 months ago

Theta minus sin theta? What does that give you

[-] TheOakTree@beehaw.org 2 points 8 months ago* (last edited 8 months ago)

(1/2)×θ×r^2

is the area of a circle sector, like a slice of pie.

(1/2)×sin(θ)×side1×side2

is the side-angle-side formula for the area of a triangle.

We know that the triangle encompassed by the sector has two sides that are equal to the radius, so we replace side1×side2 with r^2. Since the area of the arc segment is equal to the area of a sector minus the triangle, we can subtract triangle area from sector area to get

(1/2)×(θ-sin(θ))×r^2

which is the area of the arc segment, as shown with pie in the picture.

[-] ryannathans@aussie.zone 1 points 8 months ago

Is theta in radians? That's the only way I see this working

[-] TheOakTree@beehaw.org 1 points 8 months ago

Yeah, it's in radians. The degree version has a less clean format.

[-] ryannathans@aussie.zone 1 points 8 months ago* (last edited 8 months ago)

That makes way more sense, I was so confused, cheers

[-] SkybreakerEngineer@lemmy.world 2 points 8 months ago

Kepler's Equation

this post was submitted on 14 Mar 2024
162 points (93.1% liked)

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