Top 10 Trigonometric Functions for Complex Numbers in Excel

To get trigonometric functions of complex numbers in Excel is easy when you know the functions that are inbuilt for specific purposes.

Also read: Top 9 Complex Functions in Excel – A Complete Guide

Trigonometric Functions for Complex Numbers in Excel

Following is a list of complex trigonometric functions in Excel.

1. IMCOS function

The IMCOS function in Excel returns the cosine value of a complex number. The cosine of a complex number is given by: cos(x+iy) = cos(x)cosh(y) – isin(x)sinh(y).

Syntax: IMCOS(inumber),

where inumber is the complex number or the cell reference of the cell containing the complex number for which the cosine value is sought.

Select the cell where you want to display the cosine value.
Type =IMCOS(, select the cell containing the complex number and finish the formula with ).

Press the Enter key to display the result.

2. IMCOSH function

The IMCOSH function in Excel returns the hyperbolic cosine value of a complex number.

Syntax: IMCOSH(inumber),

where inumber is the complex number or the cell reference of the cell containing the complex number for which the hyperbolic cosine value is sought. The hyperbolic cosine of a complex number is given by: cosh(x+iy) = cos(y)cosh(x) + isin(y)sinh(x).

Select the cell where you want to display the hyperbolic cosine value.
Type =IMCOSH(, select the cell containing the complex number and finish the formula with ).

Press the Enter key to display the result.

3. IMCOT function

The IMCOT function in Excel returns the cotangent value of a complex number.

Syntax: IMCOT(inumber),

where inumber is the complex number or the cell reference of the cell containing the complex number for which the cotangent value is sought. The cotangent of a complex number is given by:

Select the cell where you want to display the cotangent value.
Type =IMCOT(, select the cell containing the complex number and finish the formula with ).

Press the Enter key to display the result.

4. IMCSC function

The IMCSC function in Excel returns the cosecant value of a complex number.

Syntax: IMCSC(inumber),

where inumber is the complex number or the cell reference of the cell containing the complex number for which the cosecant value is sought. The cosecant of a complex number is given by:

Select the cell where you want to display the cosecant value.
Type =IMCSC(, select the cell containing the complex number and finish the formula with ).

Press the Enter key to display the result.

5. IMCSCH function

The IMCSCH function in Excel returns the hyperbolic cosecant value of a complex number. Syntax: IMCSCH(inumber), where inumber is the complex number or the cell reference of the cell containing the complex number for which the hyperbolic cosecant value is sought. The hyperbolic cosecant of a complex number is given by:

Select the cell where you want to display the hyperbolic cosecant value.
Type =IMCSCH(, select the cell containing the complex number and finish the formula with ).

Press the Enter key to display the result.

6. IMSEC function

The IMSEC function in Excel returns the secant of a complex number. Syntax: IMSEC(inumber), where inumber is the complex number or the cell reference of the cell containing the complex number for which the secant value is sought. The secant of a complex number is given by:

Select the cell where you want to display the secant value.
Type =IMSEC(, select the cell containing the complex number and finish the formula with ).

Press the Enter key to display the result.

7. IMSECH function

The IMSECH function in Excel returns the hyperbolic secant value of a complex number.

Syntax: IMSECH(inumber),

where inumber is the complex number or the cell reference of the cell containing the complex number for which the hyperbolic secant value is sought. The hyperbolic secant of a complex number is given by:

Select the cell where you want to display the hyperbolic secant value.
Type =IMSECH(, select the cell containing the complex number and finish the formula with ).

Press the Enter key to display the result.

8. IMSIN function

The IMSIN function in Excel returns the sine value of a complex number.

Syntax: IMSIN(inumber),

where inumber is the complex number or the reference of the cell containing the complex number for which the sine value is sought. The sine of a complex number is given by:

Select the cell where you want to display the sine value.
Type =IMSIN(, select the cell containing the complex number and finish the formula with ).

Press the Enter key to display the result.

9. IMSINH function

The IMSINH function in Excel returns the hyperbolic sine value of a complex number.

Syntax: IMSINH(inumber),

where inumber is the complex number or the cell reference of the cell containing the complex number for which the hyperbolic sine value is sought. The hyperbolic sine of a complex number is given by:

Select the cell where you want to display the hyperbolic sine value.
Type =IMSINH(, select the cell containing the complex number and finish the formula with ).

Press the Enter key to display the result.

10. IMTAN function

The IMTAN function in Excel returns the tangent value of a complex number.

Syntax: IMTAN(inumber),

where inumber is the complex number or the cell reference of the cell containing the complex number for which the tangent value is sought. The tangent of a complex number is given by:

Select the cell where you want to display the tangent value.
Type =IMTAN(, select the cell containing the complex number and finish the formula with ).

Press the Enter key to display the result.

Conclusion

In this article, we learned inbuilt trigonometric functions in excel to work with complex numbers.

References