( x) =

acosx + bsinx = sqrt( a^2 + b^2 )*sin( x + arctan(a,b) )

r(θ) = ( inv(θ) of arctan( f(θ)/θ ) )/cosθ

f(x) = x*tan( inv(x) of r(x)*cos(x) )

arcsinh(x) = ln( x + sqrt( x^2 + 1 ) )

arccosh(x) = ln( x + sqrt( x^2 - 1 ) )

arctanh(x) = ln( ( 1 + x ) / ( 1 - x ) )/2