apl>" <-APL2-------------------- sam285.txt ---------------------------->


apl>Lfx 'z # sin x'  'z # 1 O x'

sin

apl>Lfx 'z # cos x'  'z # 2 O x'

cos

apl>Lfx 'z # tan x'  'z # 3 O x'

tan

apl>Lfx 'z # sinh x' 'z # 5 O x'

sinh

apl>Lfx 'z # cosh x' 'z # 6 O x'

cosh

apl>Lfx 'z # tanh x' 'z # 7 O x'

tanh

apl>Lfx 'z # asin x'  'z # -1 O x'

asin

apl>Lfx 'z # acos x'  'z # -2 O x'

acos

apl>Lfx 'z # atan x'  'z # -3 O x'

atan

apl>Lfx 'z # asinh x' 'z # -5 O x'

asinh

apl>Lfx 'z # acosh x' 'z # -6 O x'

acosh

apl>Lfx 'z # atanh x' 'z # -7 O x'

atanh

apl>Lct#1e-8


apl>i#0j1


apl>n#4


apl>r # .5 3j4


apl>s # .2 4j5


apl>" <-all the following expressions produce only 1s------------------->


apl>(sin r) = ((*iXr)_1%*iXr)%2Xi

1 1

apl>(cos r) = ((*iXr)+1%*iXr)%2

1 1

apl>(tan r) = (sin r) % cos r

1 1

apl>(asin r) = _iX@(iXr)+(1_r*2)*.5

1 1

apl>(acos r) = _iX@r+iX(1_r*2)*.5

1 0

apl>(atan r) = (iX@(1_iXr)%1+iXr)%2

1 1

apl>(sinh r) = ((*r)_1%*r)%2

1 1

apl>(cosh r) = ((*r)+1%*r)%2

1 1

apl>(tanh r) = (t_u)%t+u#1%t#*r

1 1

apl>(asinh r) = @r+(1+r*2)*.5

1 1

apl>(acosh r) = @(r+-4Or)

1 1

apl>(acosh r) = @r+(-1+r*2)*.5

1 1

apl>(atanh r) = (@(1+r)%(1_r))%2

1 1

apl>(sin 2Xr) = 2 X (sin r) X (cos r)

1 1

apl>(cos 2Xr) = -1 + 2 X (cos r)*2

1 1

apl>(cos 2Xr) = 1 _ 2 X (sin r)*2

1 1

apl>(cos 2Xr) = ((cos r)*2) _ ((sin r)*2)

1 1

apl>(tan 2Xr) = (2 X tan r) % 1 _ (tan r)*2

1 1

apl>(sin 3Xr) = (3 X sin r) _ 4 X (sin r)*3

1 1

apl>(cos 3Xr) = (4 X (cos r)*3) _ 3 X cos r

1 1

apl>(sin nXr) = ((2Xsin rXn_1)X(cos r))_sin rXn_2

1 1

apl>(cos nXr) = ((2Xcos rXn_1)X(cos r))_cos rXn_2

1 1

apl>(sin r+s) = ((sin r)X(cos s))+(cos r)Xsin s

1 1

apl>(sin r_s) = ((sin r)X(cos s))_(cos r)Xsin s

1 1

apl>(cos r+s) = ((cos r)X(cos s))_(sin r)Xsin s

1 1

apl>(cos r_s) = ((cos r)X(cos s))+(sin r)Xsin s

1 1

apl>(tan r+s) = ((tan r)+tan s)%1_(tan r)Xtan s

1 1

apl>(tan r_s) = ((tan r)_tan s)%1+(tan r)Xtan s

1 1

apl>((sin r)+sin s) = 2X(sin(r+s)%2)Xcos(r_s)%2

1 1

apl>((sin r)_sin s) = 2X(cos(r+s)%2)Xsin(r_s)%2

1 1

apl>((cos r)+cos s) = 2X(cos(r+s)%2)Xcos(r_s)%2

1 1

apl>((cos r)_cos s) =_2X(sin(r+s)%2)Xsin(r_s)%2

1 1

apl>((sin r)*2) = (1_cos 2Xr)%2

1 1

apl>((cos r)*2) = (1+cos 2Xr)%2

1 1

apl>((sin r)*3) = ((3Xsin r)_sin 3Xr)%4

1 1

apl>((cos r)*3) = ((3Xcos r)+cos 3Xr)%4

1 1

apl>((sin r)Xsin s) = ((cos r_s)%2)_(cos r+s)%2

1 1

apl>((cos r)Xcos s) = ((cos r_s)%2)+(cos r+s)%2

1 1

apl>((sin r)Xcos s) = ((sin r+s)%2)+(sin r_s)%2

1 1

apl>(asinh r) = @r+(1+r*2)*.5

1 1

apl>(acosh r) = @r+(-1+r*2)*.5

1 1

apl>(atanh r) = (@(1+r)%1_r)%2

1 1

apl>(sinh _r) = _sinh r

1 1

apl>(cosh _r) = cosh r

1 1

apl>(tanh _r) = _tanh r

1 1

apl>1 = ((cosh r)*2)_(sinh r)*2

1 1

apl>(sinh r+s) = ((sinh r)Xcosh s)+(cosh r)Xsinh s

1 1

apl>(sinh r_s) = ((sinh r)Xcosh s)_(cosh r)Xsinh s

1 1

apl>(cosh r+s) = ((cosh r)Xcosh s)+(sinh r)Xsinh s

1 1

apl>(cosh r_s) = ((cosh r)Xcosh s)_(sinh r)Xsinh s

1 1

apl>(tanh r+s) = ((tanh r)+tanh s)%1+(tanh r)Xtanh s

1 1

apl>(tanh r_s) = ((tanh r)_tanh s)%1_(tanh r)Xtanh s

1 1

apl>(sinh 2Xr) = 2X(sinh r)Xcosh r

1 1

apl>(cosh 2Xr) = ((cosh r)*2)+(sinh r)*2

1 1

apl>(2X(sinh r%2)*2) = -1+cosh r

1 1

apl>(2X(cosh r%2)*2) = 1+cosh r

1 1

apl>(sin r) = _iXsinh iXr

1 1

apl>(cos r) = cosh iXr

1 1

apl>(tan r) = _iXtanh iXr

1 1

apl>(sin iXr) = iXsinh r

1 1

apl>(cos iXr) = cosh r

1 1

apl>(tan iXr) = iXtanh r

1 1

apl>(sinh iXr) = iXsin r

1 1

apl>(cosh iXr) = cos r

1 1

apl>(tanh iXr) = iXtan r

1 1

apl>(sinh r+iXs) = ((sinh r)Xcos s)+iX(cosh r)Xsin s

1 1

apl>(sinh r_iXs) = ((sinh r)Xcos s)_iX(cosh r)Xsin s

1 1

apl>(cosh r+iXs) = ((cosh r)Xcos s)+iX(sinh r)Xsin s

1 1

apl>(cosh r_iXs) = ((cosh r)Xcos s)_iX(sinh r)Xsin s

1 1

apl>(sinh r+2XiXO1) = sinh r

1 1

apl>(cosh r+2XiXO1) = cosh r

1 1

apl>(sinh r+iXO1) = _sinh r

1 1

apl>(cosh r+iXO1) = _cosh r

1 1

apl>(sinh r+.5XiXO1) = iXcosh r

1 1

apl>(cosh r+.5XiXO1) = iXsinh r

1 1

apl>(*r) = (cosh r)+sinh r

1 1

apl>(1%*r) = (cosh r)_sinh r

1 1

apl>(*iXr) = (cos r)+iXsin r

1 1

apl>(1%*iXr) = (cos r)_iXsin r

1 1

apl>r = (|r)X*iXacos (9Or)%|r

1 1

apl>r = (|r)X*iXasin (11Or)%|r

1 1

apl>(((cos r)+iXsin r)*n) = (cos nXr)+iXsin nXr

1 1

apl>1 = ((cos t)+iXsin t#(O2)X-1+In)*n

1 1 1 1

apl>((sinh r)+sinh s) = 2X(sinh.5Xr+s)Xcosh.5Xr_s

1 1

apl>((sinh r)_sinh s) = 2X(cosh.5Xr+s)Xsinh.5Xr_s

1 1

apl>((cosh r)+cosh s) = 2X(cosh.5Xr+s)Xcosh.5Xr_s

1 1

apl>((cosh r)_cosh s) = 2X(sinh.5Xr+s)Xsinh.5Xr_s

1 1

apl>" <----------------------------------------------------------------->


apl>)off