HP 49g - Page 403

Command Reference: Part E, T-Z (1.1) 1-403
*RWR,QGH[
√
7\SH )XQFWLRQ
'HVFULSWLRQ 6TXDUH5RRW$QDO\WLF)XQFWLRQ5HWXUQVWKHSRVLWLYHVTXDUHURRWRIWKHDUJXPHQW
)RUDFRPSOH[QXPEHU[

\

WKHVTXDUHURRWLVWKLVFRPSOH[QXPEHU
ZKHUHU $%6[

\

DQG
θ
 $5*[

\


,I[

\

 WKHQWKHVTXDUHURRWLV
7KHLQYHUVHRI64LVDUHODWLRQQRWDIXQFWLRQVLQFH64VHQGVPRUHWKDQRQHDUJXPHQWWRWKH
VDPHUHVXOW7KHLQYHUVHUHODWLRQIRU64LVH[SUHVVHGE\,62/DVWKLVJHQHUDOVROXWLRQ
V
√
=
7KHIXQFWLRQ
√
LVWKHLQYHUVHRIDSDUWRI64DSDUWGHILQHGE\UHVWULFWLQJWKHGRPDLQRI64
VXFKWKDW
 HDFKDUJXPHQWLVVHQWWRDGLVWLQFWUHVXOWDQG
 HDFKSRVVLEOHUHVXOWLVDFKLHYHG7KHSRLQWVLQWKLVUHVWULFWHGGRPDLQRI64DUHFDOOHGWKH
SULQFLSDOYDOXHVRIWKHLQYHUVHUHODWLRQ7KH√IXQFWLRQLQLWVHQWLUHW\LVFDOOHGWKHSULQFL
SDOEUDQFKRIWKHLQYHUVHUHODWLRQDQGWKHSRLQWVVHQWE\√WRWKHERXQGDU\RIWKHUHVWULFWHG
GRPDLQRI64IRUPWKHEUDQFKFXWVRI√
7KHSULQFLSDOEUDQFKXVHGE\WKH+3*IRU
√
ZDVFKRVHQEHFDXVHLWLVDQDO\WLFLQWKHUHJLRQV
ZKHUHWKHDUJXPHQWVRIWKHUHDOYDOXHGLQYHUVHIXQFWLRQDUHGHILQHG7KHEUDQFKFXWIRUWKH
FRPSOH[YDOXHGVTXDUHURRWIXQFWLRQRFFXUVZKHUHWKHFRUUHVSRQGLQJUHDOYDOXHGIXQFWLRQLV
XQGHILQHG7KHSULQFLSDOEUDQFKDOVRSUHVHUYHVPRVWRIWKHLPSRUWDQWV\PPHWULHV
7KHJUDSKVEHORZVKRZWKHGRPDLQDQGUDQJHRI
√
7KHJUDSKRIWKHGRPDLQVKRZVZKHUH
WKHEUDQFKFXWRFFXUVWKHKHDY\VROLGOLQHPDUNVRQHVLGHRIWKHFXWZKLOHWKHIHDWKHUHGOLQHV
PDUNWKHRWKHUVLGHRIWKHFXW7KHJUDSKRIWKHUDQJHVKRZVZKHUHHDFKVLGHRIWKHFXWLV
PDSSHGXQGHUWKHIXQFWLRQ
x
2
y
2
,() r
θ
2
---
r,cos
θ
2
---
sin


=