## Engineering trignometric functions on complex numbers

#### Excel Function IMSINH

The IMSINH() function returns the sinh() value of a specified complex number.

The sinh defines the hyperbolic function with respect to sine.

The formula for sinh of a complex number is as given below:

 Complex Number1 IMSINH Formula 2+5i 1.02880314965993-3.60766077421316i =IMSINH(L4) 4+2.3i -18.1826174511581+20.363891561153i =IMSINH(L5) 6+5.7i 168.372551327245-111.081884528522i =IMSINH(L6) 1.4+8i -0.277075932842992+2.12800913438628i =IMSINH(L7) 2-8i -0.527708311960863-3.72215933238454i =IMSINH(L8)

#### Excel Function IMCOSH

The IMCOSH() function returns the cosh() value of a specified complex number.

The cosh defines the hyperbolic function with respect to cosine.

The formula for cosh of a complex number is as given below:

 Complex Number1 IMCOSH Formula 2+5i 1.06719265187312-3.47788448589916i =IMCOSH(L18) 4+2.3i -18.1948207221641+20.3502334937693i =IMCOSH(L19) 6+5.7i 168.374620373378-111.080519515535i =IMCOSH(L20) 1.4+8i -0.312955799433597+1.88403639451836i =IMCOSH(L21) 2-8i -0.547399600247289-3.58826425385529i =IMCOSH(L22)

#### Excel Function IMCSCH

The IMCSCH() function returns the cosech() value of a specified complex number.

The cosech defines the hyperbolic function with respect to cosecant.

The formula for cosech of a complex number is as given below:

 Complex Number1 IMCSCH Formula 2+5i 0.07310136248328+0.256341476073085i =IMCSCH(L31) 4+2.3i -0.0243965160444408-0.0273232392714327i =IMCSCH(L32) 6+5.7i 0.0041380868483831+0.00273005594936724i =IMCSCH(L33) 1.4+8i -0.0601659638955466-0.462088927880395i =IMCSCH(L34) 2-8i -0.0373388751400434+0.263367544935622i =IMCSCH(L35)

#### Excel Function IMSECH

The IMSECH() function returns the sech() value of a specified complex number.

The sech defines the hyperbolic function with respect to secant.

The formula for sech of a complex number is as given below:

 Complex Number1 IMSECH Formula 2+5i 0.0806366805126768+0.262787660369676i =IMSECH(L44) 4+2.3i -0.0244165639948333-0.0273090230455054i =IMSECH(L45) 6+5.7i 0.00413809768049731+0.00272999600020687i =IMSECH(L46) 1.4+8i -0.0857992713039738-0.516523260001578i =IMSECH(L47) 2-8i -0.0415474527144603+0.272348096978318i =IMSECH(L48)