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) + *i*sin(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

- 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)