ハートレー変換
cas ( a + b ) = cos  ( a ) cas ( b ) + sin  ( a ) cas ( − b ) = cos  ( b ) cas ( a ) + sin  ( b ) cas ( − a ) {\displaystyle {\mbox{cas}}(a+b)=\cos(a){\mbox{cas}}(b)+\sin(a){\mbox{cas}}(-b)=\cos(b){\mbox{cas}}(a)+\sin(b){\mbox{cas}}(-a)\,}
などが得られ、微分は
cas ′ ( a ) = d d a cas ( a ) = cos  ( a ) − sin  ( a ) = cas ( − a ) {\displaystyle {\mbox{cas}}'(a)={\frac {\mbox{d}}{{\mbox{d}}a}}{\mbox{cas}}(a)=\cos(a)-\sin(a)={\mbox{cas}}(-a)}
となる。