Overview of Trigonometric Functions

  • Last update:September 19, 2025
  • Sine - SIN

    1. Overview

    Syntax

    SIN(number)

    Returns the sine of a given angle.

    Parameter

    number

    The angle in radians for which you want the sine

    If the parameter value is in degrees, you should multiply it by PI()/180 to convert it to radians.

    Returned Value

    Numeric

    /

    2. Example

    Formula
    Result
    SIN(10)

    -0.544021111

    SIN(45*PI()/180)

    0.707106781

    Cosine - COS

    1. Overview

    Syntax

    COS(number)

    Returns the cosine of a given angle.

    Parameter

    number

    The angle in radians for which you want the cosine

    If the parameter value is in degrees, you should multiply it by PI()/180 to convert it to radians.

    Returned Value

    Numeric

    /

    2. Example

    Formula
    Result
    COS(0.5)

    0.877582562

    COS(30*PI()/180)

    0.866025404

    Tangent - TAN

    1. Overview

    Syntax

    TAN(number)

    Returns the tangent of a given angle.

    Parameter

    number

    The angle in radians for which you want the tangent

    If the parameter value is in degrees, you should multiply it by PI()/180 to convert it to radians.

    Returned Value

    Numeric

    /

    2. Example

    Formula
    Result
    TAN(0.8)

    1.029638557

    TAN(45*PI()/180)

    1

    Hyperbolic Sine - SINH

    1. Overview

    Syntax

    SINH(number)

    Returns the hyperbolic sine of a number.

    Parameter

    number

    Any real number

    Returned Value

    Numeric

    /

    2. Example

    Formula
    Result

    SINH(1)

    1.175201194

    SINH(-1)

    -1.175201194

    Hyperbolic Cosine - COSH

    1. Overview

    Syntax

    COSH(number)

    Returns the hyperbolic cosine of a number.

    The formula for the hyperbolic cosine is: COSH(number) = (e^x + e^(-x))/2, where e is the base of the natural logarithm and approximately equals 2.71828182845904.

    Parameter

    number

    The real number for which you want the hyperbolic cosine

    Returned Value

    Numeric

    /

    2. Example

    Formula
    Result
    COSH(3)

    10.06766200

    COSH(5)

    74.20994852

    COSH(6)

    201.7156361

    Hyperbolic Tangent - TANH

    1. Overview

    Syntax

    TANH(number)

    Returns the hyperbolic tangent of a number. 

    Parameter

    number

    Any real number

    Reurned Value

    Numeric

    /

    2. Example

    Formula
    Result
    TANH(-2)

    -0.96403

    TANH(0)

    0

    TANH(0.5)

    0.462117

    Arcsine - ASIN

    1.Overview

    Syntax

    ASIN(number)

    Returns the arcsine of a number.

    The returned arcsine value is an angle given in radians. 

    Parameter

    number

    The sine of the angle for which you want the arcsine

    The given number must be between -1 and 1 (inclusive).

    Returned Value

    Numeric

    The returned angle is between -pi/2 to pi/2 (inclusive). To express the returned angle in degrees, you should multiply the result by 180/PI().

    2.Example

    Formula
    Result
    ASIN(0.5)

    0.523598776 (pi/6 radians)

    ASIN(1)

    1.570796327 (pi/2 radians)

    ASIN(0.5)*180/PI()

    30 (degrees)

    Arccosine - ACOS

    1. Overview

    Syntax

    ACOS(number)

    Returns the arccosine of a number.

    The returned arccosine value is an angle given in radians.

    Parameter

    number

    The cosine of the angle for which you want the arccosine

    The given number must be between -1 and 1 (inclusive).

    Returned Value

    Numeric

    The returned angle value is between 0 and pi.

    To display the returned angle in degrees, you should multiply it by 180/PI().

    2. Example

    Formula
    Result
    ACOS(1)

    0 (radians)

    ACOS(0.5)

    1.047197551 (pi/3 radians)

    ACOS(0.5)*180/PI()

    60 (degrees)

    Arctangent - ATAN

    1. Overview

    Syntax

    ATAN(number)

    Returns the arctangent of a given number.

    The given number is the tangent of the returned angle expressed in radians.

    Parameter

    number

    the tangent of the returned angle

    Returned Value

    Numeric

    The returned angle is between -pi/2 and pi/2 (exclusive). If the returned angle equals -pi/2 or and pi/2, the ATAN() function returns the error: "*NUM!". To express the returned angle in degrees, you should multiply the result by 180/PI().

    2. Example

    Formula
    Result

    ATAN(-1)

    -0.785398163 (-pi/4 radians)

    ATAN(0)

    0 (radians)

    ATAN(2)*180/PI()

    63.43494882 (degrees)

    The Arctangent Value of X and Y Coordinates - ATAN2

    1. Overview

    Syntax

    ATAN2(x_num,y_num)

    Returns the arctangent value of the given x and y coordinates. The arctangent is the angle from the x-axis to a line containing the origin (0, 0) and the point (x_num, y_num). The angle is given in radians.

    Parameter

    number

    X_num: the x-coordinate of the specified point 

    Y_num: the y-coordinate of the specified point

    Returned Value

    Numeric

    A positive result represents a counterclockwise angle from the x-axis; a negative result represents a clockwise angle. ATAN2(a,b)=ATAN(b/a), except when a equals 0. If both x_num and y_num are 0, the ATAN2() function returns the error: "*DIV/0!". To express the returned angle in degrees, you should multiply the result by 180/PI(). The returned value is expressed in radians between -pi and pi, excluding -pi.

    2. Example

    Formula
    Result
    ATAN2(-2,2)

    2.356194490192345 (3 * pi/4 radians)

    ATAN2(2,2)

    0.785398163 (pi/4 radians)

    ATAN2(-2,2)*180/PI()

    135 (degrees)

    Inverse Hyperbolic Sine - ASINH

    1. Overview

    Syntax

    ASINH(number)

    Returns the inverse hyperbolic sine of a given number. The hyperbolic sine of the inverse hyperbolic sine of a specified number equals that number. That is: ASINH(SINH(number)) = number.

    Parameter

    number

    Any real number

    Returned Value

    Numeric

    /

    2. Example

    Formula
    Result
    ASINH(-5)

    -2.312438341

    ASINH(8)

    2.776472281

    ASINH(16)

    3.466711038

    Inverse Hyperbolic Cosine - ACOSH

    1. Overview

    Syntax

    ACOSH(number)

    Returns the inverse hyperbolic cosine of a given number.

    Parameter

    number

    The hyperbolic cosine of the returned value

    The value must be greater than or equal to 1.

    ACOSH(COSH(number))=number

    Returned Value

    Numeric

    /

    2.Example

    Formula

    Result

    ACOSH(1)

     0

    ACOSH(8)

    2.768659383

    ACOSH(5.5)

    2.389526435

    Inverse Hyperbolic Tangent - ATANH

    1. Overview

    Syntax

    ATANH(number)

    Returns the inverse hyperbolic tangent of a given number. The given number is the hyperbolic tangent of the returned value.

    Parameter

    number

    a real number between -1 and 1

    The given number must be between -1 to 1 (exclusive).

    ATANH(TANH(number))=number, for example, ATANH(TANH(8))=8.

    Returned Value

    Numeric

    /

    2.Example:

    Formula
    Result
    ATANH(-0.5)

    -0.549306144

    ATANH(0)

     0

    ATANH(0.7)

    0.867300528

    Converting Radians to Degrees - DEGREES

    1. Overview

    Syntax

    DEGREES(angle)

    Converts radians to degrees

    Parameter

    angle

    The angle in radians to be converted

    Returned Value

    Numeric

    /

    2. Example:

    Formula
    Result
    DEGREES(PI()/2)

    90

    DEGREES(3.1415926)

     180

    Converting Degrees to Radians - RADIANS

    1. Overview

    Syntax

    RADIANS(angle)

    Converts degrees to radians

    Parameter

    angle

    The angle in degrees to be converted

    Returned Value

    Numeric

    /

    2. Example:

    Formula
    Result
    ASIN(1)

    1.570796327 (pi/2 radians)

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