Sunday, February 16, 2020

Casio fx-3650P: Circular Segment

Casio fx-3650P: Circular Segment

Introduction





Variables:
X:  radius
Y:  angle (in degree)
C:  chord length
D:  altitude
A:  area
B:  arc length

Program 1:  Given Chord Length and Altitude

Calculate:  Radius, Angle, Area, Arc Length

? → C : ? → D : Deg :
( ( C ÷ 2 )^2 + D^2 ) ÷ ( 2D ) → X ◢
2 cos^-1 ( ( X - D ) ÷ X ) → Y ◢
X^2 ÷ 2 * ( π Y ÷ 180 - sin Y ) → A ◢
X Y π ÷ 180 → B

Example:
Input C = 8,  D = 11.75

X:  6.555851064 (radius)
Y:  284.8004594 (angle)
A:  127.5950317 (area)
B:  32.58720643 (arc length)

Program 2:  Given Radius and Angle

Calculate:  Chord Length, Altitude, Area, Arc Length

? → X : ? → Y : Deg :
2 * sin(Y ÷ 2) → C ◢
2 X ( sin(Y ÷ 4))^2 → D ◢
X^2 ÷ 2 * ( π Y ÷ 180 - sin Y ) → A ◢
X Y π ÷ 180 → B

Example:
Input X = 17.25, Y = 204

C:  33.74609223 (chord length)
D:  20.83647667 (altitude)
A:  590.2462124 (area)
B:  61.41813638 (arc length)

Source:

John W Harris and Horst Stocker.  Handbook of Mathematics and Computational Science Spring:  New York.  2006 ISBN 978-0-387-94746-4

Announcement

I am going to have surgery this week and my family is having medical issues.  I will be taking some time off in the next few weeks.  Tomorrow I have a special post reviewing the classic TI-30 from 1976. Take care everyone and thank you so much for your support.  I love doing this blog. 

Eddie

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