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#Engineering

IMSIN

Excel Functions

Get sine of complex number.

Syntax

EXCEL 
=IMSIN(complex_num)

Arguments

Parameter Description
complex_num The complex number in the form "x+yi".

Return Value

Returns the sine of the complex number.

Details

The Excel IMSIN function returns the sine of a complex number. For instance, given "1+1i" as input, the function returns the complex number equal to the sine of the input. Given real number input, the function behaves like the sine function. For example, given π + 0i as input the function returns 3.23108914886517E-15 (approximately zero). The sine of π is zero, but due to floating-point precision, it returns a very small number close to zero. Mathematically, the sine of a complex number can be represented using a combination of the standard and hyperbolic trigonometric functions. If B6 contains a complex number in the form "x+yi", this is equivalent to the following formula. Alternatively, the sine of a complex number can be defined in terms of the exponential function, where "z=x+yi".

Examples

Example 1

The Excel IMSIN function returns the sine of a complex number. For instance, given "1+1i" as input, the function returns the complex number equal to t

EXCEL 
=IMSIN("1+1i") // returns 1.29845758141598+0.634963914784736i
Example 2

Given real number input, the function behaves like the sine function. For example, given π + 0i as input the function returns 3.23108914886517E-15 (ap

EXCEL 
=IMSIN(COMPLEX(PI(),0)) // returns 3.23108914886517E-15
Explanation

If B6 contains a complex number in the form "x+yi", this is equivalent to the following formula.

EXCEL 
=COMPLEX(
    SIN(IMREAL(B6))*COSH(IMAGINARY(B6)),
    COS(IMREAL(B6))*SINH(IMAGINARY(B6))
)
Explanation

If B6 contains a complex number in the form "x+yi", this is equivalent to the following formula.

EXCEL 
=IMDIV(
    IMSUB(
        IMEXP(IMPRODUCT(COMPLEX(0,1), B6)),
        IMEXP(IMPRODUCT(COMPLEX(0,-1), B6))
    ),
    COMPLEX(0, 2)
)

See Also

IMCOS COMPLEX IMREAL IMAGINARY SIN