103
and from (9.17), the value of S5 can be computed, if S4 is not zero,
S5 1 tz/S4 (9.25)
and
C5 = u5 Trig(S5) (9.26)
where u5 = 1 or -1 is another sign ambiguity. This
additional sign ambiguity can be avoided if more equations involving 92 are considered. Indeed, Eq. (9.15) allows us to derive expressions for ipx and 1py as
IPx = R2(d5 R4z + d3 z + a2 x). x and
py = R2(d5 R4z + d3 z + a2 x) y.
These last equalities yield a system of two equations that can readily be solved for S2 and C2;
S2 = (d3 1Px + k0 Pz)/(d32+kO2), (9.27)
C2 = (kO IPx -d3 Pz)/(d32+k02), (9.28)
where kO = (a2 + d5 S4). The value of C5 can then be
obtained from either the expression for Ity,
it = R2 R3 R4 R5 z y
which, after using properties (4.5) and (4.6), gives
..