# Geometry/Trig question

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This question doesn't really relate to games too much. Just something some co-workers and myself tried to figure out. If I have a circle, we'll say it has a diameter of 10", and I also have a chord of .75", how do I figure the arc length between the chords intersecting points of the circle. I know arc lengh = radius * theta. However how do I figure theta given chord length and radius. Thank you for any help.

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Consider, not the chord, but the top half of the chord. Note that its two ends and the center of the circle form a right triangle. Use trig to figure out the angle at the center of the circle. Double it to find the full angle subtended by the full chord. Use that to determine the arclength.

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for a unit circle and chord length d u have:
theta = arcsin(d/2)

I guess that's all there is into it

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Folks,

Please advise only. This problem is academic (whether for school or work) and off topic, so I don't really want to see straight answers. Keep it educational.

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Quote:
 Original post by grhodes_at_workFolks,Please advise only. This problem is academic (whether for school or work) and off topic, so I don't really want to see straight answers. Keep it educational.

I realize this question does sound academic in nature. I assure you however, that this problem arose strictly from my inquisitiveness. I do work in a research and development environment, and find it healthy to stimulate the mind of those that I work with every once and a while. I just thought it would be an interesting problem to solve.

With that being said, I realize we need to honor the wishes of the moderator regardless. However, when I try calculating this, I still get inaccurate results, so yes I already know the answer.

When I calculate the central angle using arcsine, I seem to get a fairly odd answer.
2*arcsine(.375/5) = 26.691
This can't be radians, can it? There's only 2pi radians in a circle right?
Using a calculator I found online, it says the central angle should be 8.6024 degrees or 0.1501401 radians.

EDIT: I just tried calculating this on my TI-89 and everything works fine, so I guess that brings in the question, how do I calculate arcsine on windows calculator.
I'm using windows calc. .375/5 sin and 1/X to get arcsine(.375/5), is this the correct method?

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Original post by boohillie
Quote:
 Original post by grhodes_at_workWhen I calculate the central angle using arcsine, I seem to get a fairly odd answer.2*arcsine(.375/5) = 26.691This can't be radians, can it? There's only 2pi radians in a circle right?Using a calculator I found online, it says the central angle should be 8.6024 degrees or 0.1501401 radians.I'm using windows calc. .375/5 sin and 1/X to get arcsine(.375/5), is this the correct method?

No. Windows Calc doesn't have arcsin. Grab SpeedCrunch. Beats Calc pants down.

If you really need to use Calc, you can always approximate arcsin with a power series: x + 1/6 x^3 + 3/40 x^5 (works when -1<x<1)

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I found it. There is a Inv check box that if checked before performing the sine function yields the correct results. Thank you for the help.

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Quote:
 Original post by boohillieI found it. There is a Inv check box that if checked before performing the sine function yields the correct results. Thank you for the help.

Or you can do that.

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Quote:
 Original post by boohillieI realize this question does sound academic in nature. I assure you however, that this problem arose strictly from my inquisitiveness. I do work in a research and development environment, and find it healthy to stimulate the mind of those that I work with every once and a while. I just thought it would be an interesting problem to solve.

Understood. That's why I left the thread open. I'm softer now than I used to be, but my core ideals and goals for the forum still stand. I'd rather have replies here that teach problem solving, when the problem is an academic type problem.

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