" <-APL2-------------------- sam285.txt ---------------------------->
Lfx 'z # sin x'  'z # 1 O x'
Lfx 'z # cos x'  'z # 2 O x'
Lfx 'z # tan x'  'z # 3 O x'
Lfx 'z # sinh x' 'z # 5 O x'
Lfx 'z # cosh x' 'z # 6 O x'
Lfx 'z # tanh x' 'z # 7 O x'
Lfx 'z # asin x'  'z # -1 O x'
Lfx 'z # acos x'  'z # -2 O x'
Lfx 'z # atan x'  'z # -3 O x'
Lfx 'z # asinh x' 'z # -5 O x'
Lfx 'z # acosh x' 'z # -6 O x'
Lfx 'z # atanh x' 'z # -7 O x'
Lct#1e-8
i#0j1
n#4
r # .5 3j4
s # .2 4j5
" <-all the following expressions produce only 1s------------------->
(sin r) = ((*iXr)_1%*iXr)%2Xi
(cos r) = ((*iXr)+1%*iXr)%2
(tan r) = (sin r) % cos r
(asin r) = _iX@(iXr)+(1_r*2)*.5
(acos r) = _iX@r+iX(1_r*2)*.5
(atan r) = (iX@(1_iXr)%1+iXr)%2
(sinh r) = ((*r)_1%*r)%2
(cosh r) = ((*r)+1%*r)%2
(tanh r) = (t_u)%t+u#1%t#*r
(asinh r) = @r+(1+r*2)*.5
(acosh r) = @(r+-4Or)
(acosh r) = @r+(-1+r*2)*.5
(atanh r) = (@(1+r)%(1_r))%2
(sin 2Xr) = 2 X (sin r) X (cos r)
(cos 2Xr) = -1 + 2 X (cos r)*2
(cos 2Xr) = 1 _ 2 X (sin r)*2
(cos 2Xr) = ((cos r)*2) _ ((sin r)*2)
(tan 2Xr) = (2 X tan r) % 1 _ (tan r)*2
(sin 3Xr) = (3 X sin r) _ 4 X (sin r)*3
(cos 3Xr) = (4 X (cos r)*3) _ 3 X cos r
(sin nXr) = ((2Xsin rXn_1)X(cos r))_sin rXn_2
(cos nXr) = ((2Xcos rXn_1)X(cos r))_cos rXn_2
(sin r+s) = ((sin r)X(cos s))+(cos r)Xsin s
(sin r_s) = ((sin r)X(cos s))_(cos r)Xsin s
(cos r+s) = ((cos r)X(cos s))_(sin r)Xsin s
(cos r_s) = ((cos r)X(cos s))+(sin r)Xsin s
(tan r+s) = ((tan r)+tan s)%1_(tan r)Xtan s
(tan r_s) = ((tan r)_tan s)%1+(tan r)Xtan s
((sin r)+sin s) = 2X(sin(r+s)%2)Xcos(r_s)%2
((sin r)_sin s) = 2X(cos(r+s)%2)Xsin(r_s)%2
((cos r)+cos s) = 2X(cos(r+s)%2)Xcos(r_s)%2
((cos r)_cos s) =_2X(sin(r+s)%2)Xsin(r_s)%2
((sin r)*2) = (1_cos 2Xr)%2
((cos r)*2) = (1+cos 2Xr)%2
((sin r)*3) = ((3Xsin r)_sin 3Xr)%4
((cos r)*3) = ((3Xcos r)+cos 3Xr)%4
((sin r)Xsin s) = ((cos r_s)%2)_(cos r+s)%2
((cos r)Xcos s) = ((cos r_s)%2)+(cos r+s)%2
((sin r)Xcos s) = ((sin r+s)%2)+(sin r_s)%2
(asinh r) = @r+(1+r*2)*.5
(acosh r) = @r+(-1+r*2)*.5
(atanh r) = (@(1+r)%1_r)%2
(sinh _r) = _sinh r
(cosh _r) = cosh r
(tanh _r) = _tanh r
1 = ((cosh r)*2)_(sinh r)*2
(sinh r+s) = ((sinh r)Xcosh s)+(cosh r)Xsinh s
(sinh r_s) = ((sinh r)Xcosh s)_(cosh r)Xsinh s
(cosh r+s) = ((cosh r)Xcosh s)+(sinh r)Xsinh s
(cosh r_s) = ((cosh r)Xcosh s)_(sinh r)Xsinh s
(tanh r+s) = ((tanh r)+tanh s)%1+(tanh r)Xtanh s
(tanh r_s) = ((tanh r)_tanh s)%1_(tanh r)Xtanh s
(sinh 2Xr) = 2X(sinh r)Xcosh r
(cosh 2Xr) = ((cosh r)*2)+(sinh r)*2
(2X(sinh r%2)*2) = -1+cosh r
(2X(cosh r%2)*2) = 1+cosh r
(sin r) = _iXsinh iXr
(cos r) = cosh iXr
(tan r) = _iXtanh iXr
(sin iXr) = iXsinh r
(cos iXr) = cosh r
(tan iXr) = iXtanh r
(sinh iXr) = iXsin r
(cosh iXr) = cos r
(tanh iXr) = iXtan r
(sinh r+iXs) = ((sinh r)Xcos s)+iX(cosh r)Xsin s
(sinh r_iXs) = ((sinh r)Xcos s)_iX(cosh r)Xsin s
(cosh r+iXs) = ((cosh r)Xcos s)+iX(sinh r)Xsin s
(cosh r_iXs) = ((cosh r)Xcos s)_iX(sinh r)Xsin s
(sinh r+2XiXO1) = sinh r
(cosh r+2XiXO1) = cosh r
(sinh r+iXO1) = _sinh r
(cosh r+iXO1) = _cosh r
(sinh r+.5XiXO1) = iXcosh r
(cosh r+.5XiXO1) = iXsinh r
(*r) = (cosh r)+sinh r
(1%*r) = (cosh r)_sinh r
(*iXr) = (cos r)+iXsin r
(1%*iXr) = (cos r)_iXsin r
r = (|r)X*iXacos (9Or)%|r
r = (|r)X*iXasin (11Or)%|r
(((cos r)+iXsin r)*n) = (cos nXr)+iXsin nXr
1 = ((cos t)+iXsin t#(O2)X-1+In)*n
((sinh r)+sinh s) = 2X(sinh.5Xr+s)Xcosh.5Xr_s
((sinh r)_sinh s) = 2X(cosh.5Xr+s)Xsinh.5Xr_s
((cosh r)+cosh s) = 2X(cosh.5Xr+s)Xcosh.5Xr_s
((cosh r)_cosh s) = 2X(sinh.5Xr+s)Xsinh.5Xr_s
" <----------------------------------------------------------------->
)off