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Functions
Reading time: 3minThese commands let you use trigonometric, inverse trigonometric, hyperbolic, exponential, logarithmic, and root functions in expressions and logic. They are useful for defining function behavior, evaluating expressions at specific inputs, and building conditions based on function properties.
Tip: For practical examples showing how these functions are used when generating exercises, see the Examples section.
Function Reference
arccsc
Description
Given a real number x in the interval (-∞,-1]∪[1,+∞), returns the angle whose cosecant is x.
Syntax
arccsc(Real)Returns
An angle whose cosecant equals x.
arccos
Description
Given a real number x with -1 ≤ x ≤ 1, returns the angle whose cosine is x.
Syntax
arccos(Real)Returns
An angle whose cosine equals x.
arccot
Description
Given a real number x, returns the angle whose cotangent is x. The returned value is in the interval (0, π).
Syntax
arccot(Real)Returns
An angle in (0, π) whose cotangent equals x.
arcsec
Description
Given a real number x in the interval (-∞,-1]∪[1,+∞), returns the angle whose secant is x. The returned value is in the interval shown below.
Syntax
arcsec(Real)Returns
An angle whose secant equals x (with the platform-defined principal range shown above).
Fix needed
Your snippet shows the function name as arcsec, but the code sample under it incorrectly shows arccot(Real). That is a copy-paste error.
arcsin
Description
Given a real number x with -1 ≤ x ≤ 1, returns the angle whose sine is x. The returned value is in the interval shown below.
Syntax
arcsin(Real)Returns
An angle whose sine equals x (with the platform-defined principal range shown above).
log2
Description
Given a positive real number x, returns its binary logarithm.
Syntax
log2(Real)Returns
log₂(x).
csc
Description
Given a real number x that is not a multiple of π, returns csc(x). The result is in (-∞,-1]∪[1,+∞).
Syntax
csc(Real)Returns
csc(x).
cos
Description
Given a real number x, returns cos(x). The result is in [-1, 1].
Syntax
cos(Real)Returns
cos(x).
cot
Description
Given a real number x that is not a multiple of π, returns cot(x).
Syntax
cot(Real)Returns
cot(x).
log
Description
Given a positive real number x, returns log(x) (platform-defined base).
Syntax
log(Real)Returns
log(x).
Note
Your docs list both log and ln, so this log function might be base-10 or another base depending on the system. If you want the natural logarithm explicitly, use ln.
New function
Description
Defines a new custom function using assignment without evaluation. On the left side, write the function name and parameters. On the right side, write the function expression. Use := (not =).
Syntax
name(var1, var2, ...):= expressionExamples
g(x):= x+3
f(x):= integral(x+3)+integral(x)
h(x,y,z):= x+y+zFix needed
Your snippet says “You are allow to create new functions.” It should be “You are allowed to create new functions.”
cosh
Description
Given a real number x, returns cosh(x). The result is in [1, +∞).
Syntax
cosh(Real)Returns
cosh(x).
sinh
Description
Given a real number x, returns sinh(x).
Syntax
sinh(Real)Returns
sinh(x).
tanh
Description
Given a real number x, returns tanh(x). The result is in (-1, 1).
Syntax
tanh(Real)Returns
tanh(x).
arcosh
Description
Given a real number x in the interval [1, +∞), returns the number whose hyperbolic cosine is x. The result is in [0, +∞).
Syntax
arcosh(Real)Returns
The inverse hyperbolic cosine of x.
arsinh
Description
Given a real number x, returns the number whose hyperbolic sine is x.
Syntax
arsinh(Real)Returns
The inverse hyperbolic sine of x.
artanh
Description
Given a real number x in the interval (-1, 1), returns the number whose hyperbolic tangent is x.
Syntax
artanh(Real)Returns
The inverse hyperbolic tangent of x.
ln
Description
Given a positive real number x, returns ln(x) (natural logarithm).
Syntax
ln(Real)Returns
ln(x).
Fix needed
Your snippet shows the function header as ln, but the code sample under it incorrectly shows artanh(Real). That is a copy-paste error.
root
Description
Given a real number x and a natural number n, computes the nth root of x. The expression definition is shown below.
Syntax
root(Natural, Real)Returns
The nth root of x.
sec
Description
Given a real number x that is not an odd multiple of π/2, returns sec(x). The result is in (-∞,-1]∪[1,+∞).
Syntax
sec(Real)Returns
sec(x).
sin
Description
Given a real number x, returns sin(x). The result is in [-1, 1].
Syntax
sin(Real)Returns
sin(x).
sqrt
Description
Given a real number x, returns its square root.
Syntax
sqrt(Real)Returns
√x.
tan
Description
Given a real number x that is not an odd multiple of π/2, returns tan(x).
Syntax
tan(Real)Returns
tan(x).