sin | Sine | asin | Inverse sine |
cos | Cosine | acos | Inverse cosine |
tan | Tangent | atan | Inverse tangent |
The basic trigonometric functions can be defined in terms of a right triangle. For the angle x at one apex of the right triangle the functions can be defined by:
The sine function, denoted by sin, is de?ned as:
sin(x) = opposite / hypotenuse
The cosine function, denoted by cos, is de?ned as:
cos(x) = adjacent / hypotenuse
The tangent function, denoted by tan, is de?ned as:
tan(x) = opposite / adjacent = sin(x) / cos(x)
Syntax
cos(x)
cos x
:cos x
Examples
cos(1) = 0.540
If the angle unit is set to degrees: cos(45) = 0.707.
If the angle unit is set to grads: cos(45) = 0.760.
In mathematics, the inverse trigonometric functions or cyclometric functions are the inverse functions of the trigonometric functions, though they do not meet the official definition for inverse functions as their ranges are subsets of the domains of the original functions.
The following table gives the inverse trigonometric function (principal value branches) along with their domains and ranges.
Function Name |
Abbreviation Functions |
Alternate Notations |
Domain of x | Range of Principal Values |
---|---|---|---|---|
arcsine | y = arcsin x | y = asin x | -1 ≤ x ≤ 1 | -π/2 ≤ y ≤ π/2 |
arccosine | y = arccos x | y = acos x | -1 ≤ x ≤ 1 | 0 ≤ y ≤ π |
arctangent | y = arctan x | y = atan x | -∞ < x < ∞ | -π/2 < y < π/2 |
Syntax
arccos(x)
arccos x
:arccos x
acos(x)
acos x
:acos x
x is the cosine of the angle you want and must be from -1 to 1.
Examples
acos(0.5) = 1.0472 radians
If the angle unit is set to degrees: acos(0.5) = 60 degrees.
If the angle unit is set to grads: acos(0.5) = 66.7 grads.
sec | Secant | asec | Inverse secant |
csc | Cosecant | acsc | Inverse cosecant |
cot | Cotangent | acot | Inverse cotangent |
The cosecant csc(x), or cosec(x), is the reciprocal of sin(x), i.e. the ratio of the length of the hypotenuse to the length of the opposite side:
csc(x) = hypotenuse / opposite = 1 / sin(x)
The inverse cosecant satisfies
acsc(x) = asin(1/x)
The secant sec(A) is the reciprocal of cos(A), i.e. the ratio of the length of the hypotenuse to the length of the adjacent side:
sec(x) = hypotenuse / adjacent = 1 / cos(x)
The inverse secant satisfies
asec(x) = acos(1/x)
cotangent
cot(x) = adjacent / opposite = cos(x) / sin(x) = 1 / tan(x)
Syntax
csc(x)
csc x
:csc x
cosec(x)
cosec x
:cosec x
x is the cosine of the angle you want and must be from -1 to 1.
Examples
csc(30) = -1.01211335307018
If the angle unit is set to degrees: csc(30) = 2.
If the angle unit is set to grads: csc(30) = 2.20268926458527.
The following table gives the inverse trigonometric function (principal value branches) along with their domains and ranges.
Function Name |
Abbreviation Functions |
Alternate Notations |
Domain of x | Range of Principal Values |
---|---|---|---|---|
arcsecant | y = arcsec x | y = asec x | -∞ < x < ∞ | 0 ≤ y < π/2 or π/2 < y ≤ π |
arccosecant | y = arccsc x | y = acsc x | -∞ < x < ∞ | -π/2 ≤ y < 0 or 0 < y ≤ π/2 |
arccotangent | y = arccot x | y = acot x | -∞ < x < ∞ | -π/2 < y < 0 or 0 < y ≤ π/2 |
Syntax
acsc(x)
acsc x
:acsc x
acosec(x)
acosec x
:acosec x
Examples
acsc(1) = 1.5707963267949
If the angle unit is set to degrees: acsc(1) = 90 degrees.
If the angle unit is set to grads: acsc(1) = 100 grads.
sinh | Hyperbolic sine | asinh | Inverse hyperbolic sine |
cosh | Hyperbolic cosine | acosh | Inverse hyperbolic cosine |
tanh | Hyperbolic tangent | atanh | Inverse hyperbolic tangent |
coth | Hyperbolic cotangent | acoth | Inverse hyperbolic cotangent |
The hyperbolic functions have similar names to the trigonmetric functions, but they are de?ned in terms of the exponential function. Unlike trigonmetric functions, hyperbolic functions are not periodic!
The hyperbolic sine, denoted sinh, is de?ned as:
sinh(x) = (ex - e-x) / 2
The hyperbolic cosine, denoted cosh, is de?ned as:
cosh(x) = (ex + e-x) / 2
The hyperbolic tangent, denoted tanh, is de?ned as:
tanh(x) = (ex - e-x) / (ex + e-x) = sinh(x) / cosh(x)
The hyperbolic cotangent, denoted coth, is de?ned as:
coth(x) = (ex + e-x) / (ex - e-x) = cosh(x) / sinh(x)
The hyperbolic secant, and hyperbolic cosecant functions are not included in c4c but you can simply calculate these yourself
hyperbolic secant (x) = 1 / cosh (x)
hyperbolic cosecant (x) = 1 / sinh (x)
Syntax
sinh(x)
cosh x
:tanh x
asinh(x)
acosh x
:atanh x
Examples
sinh(1) = 1.5707963267949 sinh(90) = 6.1020164715892e+038 cosh(1) = 1.54308063481524 cosh(90) = 6.1020164715892e+038
The required number argument x can be any valid numeric expression and changing the mode to DEG or GRAD will have no effects.
Citing this page:
Generalic, Eni. "C4C Help: Insert trigonometric functions." EniG. Periodic Table of the Elements. KTF-Split, 27 Oct. 2022. Web. {Date of access}. <https://www.periodni.com/enig/c4c_help/insert_trig_functions.html>.
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