trig.txt
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Transcript of trig.txt
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Trig functions diagram
A \ | \ | \ | \ | \ B |_______ \ E | ------__\ C |---------------/ \ \ | /| \ \ | / | \ \ | / | \ \ | / | \ \ | / | \ \ | / | \ \ | / | | \ | / | \ \ | / | | \ | / | \ \ | / | | \ | / | \ \
| / | | \ | / | | \ |/ THETA | | \ D --------------------------------------------------------------------
F G H
Assume BEG is a 90 degree arc of a circle with the center at D,Theta is angle FDE, AD is perpenducular to CE and DH, DH is perpendicularto FE, AH is tangent to the arc and thus perpendicular to DE, and the radiusof the arc is of length 1: then:
DE = DG = DB = 1
FE = DC = sine(theta)DF = CE = cosine(theta)EH = tangent(theta)AE = cotangent(theta)DH = secant(theta)AD = cosecant(theta)FG = versine(theta) = 1 - cosine(theta)BC = coversine(theta) = 1 - sine(theta)GH = exsecant(theta) = secant(theta) - 1AB = coexsecant(theta) = 1 - cosecant(theta)
haversine(theta) = versine(theta)/2 hacoversine(theta) (cohaversine?) = coversine(theta)/2
or nicer to look at, the labeled diagram (except for the vertical unit, andcosecant) :
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coexsecant | \ cotangent | \ |_______ \coversine | ------__\ |---------------/ \ \ | /| \ \ | / | \ \ | / | \ \ | / | \ \ | / | \ \ | / | \ \ tangent | one/ | | \ | / | \ \ sine | / |sine | \ | / | \ \ | / | | \ | / | \ \ | / | | \ | / | | \ |/ THETA | | \ -------------------------------------------------------------------- cosine versine exsecant
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A - \ /|\ | \ | | \ | coexsecant | \ cotangent (AE)
| (AB) | \ | B |_______ \ E| coversine | ------__\
| (BC) C |---------------/ \ \ | | /| \ \ | | / | \ \ | | / | \ \cosecant | | / | \ \ | | / | \ \ | | / | \ \ tangent (EH) | | one/ | | \ | | / | \ \ | sine | / |sine | \
| (CD) | / | (EF) \ \ | | / | | \ | | / | \ \ | | / | |\ | | / | |
\ \|/ |/ THETA | |
\ - ----------------------------------------------------------
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---------- D cosine F versine G exsecant
H (DF) (FG) (GH) ||
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-------------------------------------------------------------------------------Charles W. Grant, Ph.D. [email protected] Livermore national Laboratory