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 ).
![Top 10 Trigonometric Functions for Complex Numbers in Excel 3 trigonometric functions in Excel](https://quickexcel.com/wp-content/uploads/2021/08/imcos-formula.jpg)
- Press the Enter key to display the result.
![Top 10 Trigonometric Functions for Complex Numbers in Excel 4 trigonometric functions in Excel](https://quickexcel.com/wp-content/uploads/2021/08/imcos-result.jpg)
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 ).
![Top 10 Trigonometric Functions for Complex Numbers in Excel 5 trigonometric functions in Excel](https://quickexcel.com/wp-content/uploads/2021/08/imcosh-formula.jpg)
- Press the Enter key to display the result.
![Top 10 Trigonometric Functions for Complex Numbers in Excel 6 trigonometric functions in Excel](https://quickexcel.com/wp-content/uploads/2021/08/imcosh-result.jpg)
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:
![Top 10 Trigonometric Functions for Complex Numbers in Excel 7 cotangent formula](https://quickexcel.com/wp-content/uploads/2021/08/cotangent-formula.jpg)
- 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 ).
![Top 10 Trigonometric Functions for Complex Numbers in Excel 8 imcot formula](https://quickexcel.com/wp-content/uploads/2021/08/imcot-formula.jpg)
- Press the Enter key to display the result.
![Top 10 Trigonometric Functions for Complex Numbers in Excel 9 imcot result](https://quickexcel.com/wp-content/uploads/2021/08/imcot-result.jpg)
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:
![Top 10 Trigonometric Functions for Complex Numbers in Excel 10 cosec formula](https://quickexcel.com/wp-content/uploads/2021/08/cosec-formula.jpg)
- 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 ).
![Top 10 Trigonometric Functions for Complex Numbers in Excel 11 imcsc formula](https://quickexcel.com/wp-content/uploads/2021/08/imcsc-formula.jpg)
- Press the Enter key to display the result.
![Top 10 Trigonometric Functions for Complex Numbers in Excel 12 imcsc result](https://quickexcel.com/wp-content/uploads/2021/08/imcsc-result.jpg)
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:
![Top 10 Trigonometric Functions for Complex Numbers in Excel 13 csch formula](https://quickexcel.com/wp-content/uploads/2021/08/csch-formula.jpg)
- 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 ).
![Top 10 Trigonometric Functions for Complex Numbers in Excel 14 imcsch formula](https://quickexcel.com/wp-content/uploads/2021/08/imcsch-formula.jpg)
- Press the Enter key to display the result.
![Top 10 Trigonometric Functions for Complex Numbers in Excel 15 imcsch result](https://quickexcel.com/wp-content/uploads/2021/08/imcsch-result.jpg)
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:
![Top 10 Trigonometric Functions for Complex Numbers in Excel 16 secant formula](https://quickexcel.com/wp-content/uploads/2021/08/secant-formula.jpg)
- 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 ).
![Top 10 Trigonometric Functions for Complex Numbers in Excel 17 imsec formula](https://quickexcel.com/wp-content/uploads/2021/08/imsec-formula.jpg)
- Press the Enter key to display the result.
![Top 10 Trigonometric Functions for Complex Numbers in Excel 18 imsec result](https://quickexcel.com/wp-content/uploads/2021/08/imsec-result.jpg)
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:
![Top 10 Trigonometric Functions for Complex Numbers in Excel 19 sech formula](https://quickexcel.com/wp-content/uploads/2021/08/sech-formula.jpg)
- 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 ).
![Top 10 Trigonometric Functions for Complex Numbers in Excel 20 imsech formula](https://quickexcel.com/wp-content/uploads/2021/08/imsech-formula.jpg)
- Press the Enter key to display the result.
![Top 10 Trigonometric Functions for Complex Numbers in Excel 21 imsech result](https://quickexcel.com/wp-content/uploads/2021/08/imsech-result.jpg)
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:
![Top 10 Trigonometric Functions for Complex Numbers in Excel 22 sine formula](https://quickexcel.com/wp-content/uploads/2021/08/sine-formula.jpg)
- 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 ).
![Top 10 Trigonometric Functions for Complex Numbers in Excel 23 imsin formula](https://quickexcel.com/wp-content/uploads/2021/08/imsin-formula.jpg)
- Press the Enter key to display the result.
![Top 10 Trigonometric Functions for Complex Numbers in Excel 24 imsin result](https://quickexcel.com/wp-content/uploads/2021/08/imsin-result.jpg)
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:
![Top 10 Trigonometric Functions for Complex Numbers in Excel 25 sinh formula](https://quickexcel.com/wp-content/uploads/2021/08/sinh-formula.jpg)
- 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 ).
![Top 10 Trigonometric Functions for Complex Numbers in Excel 26 imsinh formula](https://quickexcel.com/wp-content/uploads/2021/08/imsinh-formula.jpg)
- Press the Enter key to display the result.
![Top 10 Trigonometric Functions for Complex Numbers in Excel 27 imsinh result](https://quickexcel.com/wp-content/uploads/2021/08/imsinh-result.jpg)
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:
![Top 10 Trigonometric Functions for Complex Numbers in Excel 28 tan formula](https://quickexcel.com/wp-content/uploads/2021/08/tan-formula.jpg)
- 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 ).
![Top 10 Trigonometric Functions for Complex Numbers in Excel 29 imtan formula](https://quickexcel.com/wp-content/uploads/2021/08/imtan-formula.jpg)
- Press the Enter key to display the result.
![Top 10 Trigonometric Functions for Complex Numbers in Excel 30 imtan result](https://quickexcel.com/wp-content/uploads/2021/08/imtan-result.jpg)
Conclusion
In this article, we learned inbuilt trigonometric functions in excel to work with complex numbers.
References
- IMCOS function – Office Support (microsoft.com)
- IMCOSH function – Office Support (microsoft.com)
- IMCOT function – Office Support (microsoft.com)
- IMCSC function – Office Support (microsoft.com)
- IMCSCH function – Office Support (microsoft.com)
- IMSEC function – Office Support (microsoft.com)
- IMSECH function – Office Support (microsoft.com)
- IMSIN function – Office Support (microsoft.com)
- IMSINH function – Office Support (microsoft.com)
- IMTAN function – Office Support (microsoft.com)