三角関数 (3回目)
2021/9/29(水)
三角関数 (3回目)
tanh-1(x)をlogで表す
(log = loge とする)
sinh(t) = {exp(t)-exp(-t)}/2
cosh(t) = {exp(t)+exp(-t)}/2
tanh(t) = sinh(t)/cosh(t)
x = tanh(t)と置くと
x = {exp(t)-exp(-t)}/{exp(t)+exp(-t)}
xexp(t)+xexp(-t) = exp(t)-exp(-t)
xexp(t)-exp(t) = -exp(-t)-xexp(-t)
(x-1)exp(t) = -(x+1)exp(-t)
exp2(t) = -(x+1)/(x-1)
exp(2t) = (1+x)/(1-x)
t = log{(1+x)/(1-x)}/2
tanh-1(x) = log{(1+x)/(1-x)}/2
三角関数 (3回目)
tanh-1(x)をlogで表す
(log = loge とする)
sinh(t) = {exp(t)-exp(-t)}/2
cosh(t) = {exp(t)+exp(-t)}/2
tanh(t) = sinh(t)/cosh(t)
x = tanh(t)と置くと
x = {exp(t)-exp(-t)}/{exp(t)+exp(-t)}
xexp(t)+xexp(-t) = exp(t)-exp(-t)
xexp(t)-exp(t) = -exp(-t)-xexp(-t)
(x-1)exp(t) = -(x+1)exp(-t)
exp2(t) = -(x+1)/(x-1)
exp(2t) = (1+x)/(1-x)
t = log{(1+x)/(1-x)}/2
tanh-1(x) = log{(1+x)/(1-x)}/2
