Rearranging an equation to solve for a variable

Question

In the equation below, I need to solve for $t$. Can anyone assist with rearranging the equation? My algebra skills have wilted over the years as I spent more time in front of engineering / CAD / GIS applications. Thanks!

$$ s=4r(1-\cos\frac{t}{2}) $$

t=2*arccos[1-(s/4r)]. I guess someone can post an answer with Latex formatting. — Manan, May 19 '20 at 03:04
By the way, you may find the Wikipedia plot summary useful, particularly the Equations section. — Brian Tung, May 19 '20 at 03:10

score 2 · Accepted Answer · answered May 19 '20 at 03:05

2

$$ s = 4r\left(1-\cos \frac{t}{2}\right) $$ $$ \frac{s}{4r} = 1-\cos\frac{t}{2} $$ $$ 1-\frac{s}{4r} = \cos\frac{t}{2} $$ $$ \arccos \left(1-\frac{s}{4r}\right) = \frac{t}{2} $$ $$ 2\arccos \left(1-\frac{s}{4r}\right) = t $$

answered May 19 '20 at 03:05

Brian Tung

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Rearranging an equation to solve for a variable

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