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Miscellaneous
Functions
Reading time: 2minThese commands allow you to incorporate trigonometric, inverse trigonometric, hyperbolic, exponential, logarithmic, and root functions into your statements. You can use them to define function behaviors, generate values for specific inputs, or create conditions based on function properties.
Example classroom uses
- Generate random angles or side lengths in a right triangle and use trigonometric functions to calculate missing values.
- Create problems involving exponential growth or decay, or logarithmic scales.
- Generate numbers and ask students to find their roots, or create logicals that ensure a random variable's root is an integer.
- Define a custom function with random parameters and ask students to evaluate it at a given point, with the logical checking their computation
👉Need concrete examples? Check out the Examples section to see how these functions are used in real exercises. It’s a great place to see how to combine random value generation, conditions, and solution logic in context.
Functions
arccsc
Given a real number x in the interval (-∞,-1]∪[1,+∞), returns the angle whose cosecant is x.
arccsc(Real) arccos
Given a number x between -1 and 1, returns the angle whose cosine is x.
arccos(Real) arccot
Given a number x, returns the angle whose cotangent is x. Returns a number in the interval (0,π).
arccot(Real) arcsec
Given a number x in the interval (-∞,-1]∪[1,+∞), returns the angle whose secant is x. Returns a number in the interval 
.
arccot(Real) arcsin
Given a number x between -1 and 1, returns the angle whose sine is x. Returns a number in the interval 
.
arcsin(Real) log2
Given a positive number x, returns its binary logarithm.
log2(Real) csc
Given a real number x that is not a multiple of π, returns csc(x). Returns a number in the interval (-∞,-1]∪[1,+∞).
csc(Real) cos
Given a number x, returns cos(x). Returns a number in the interval [-1,1].
cos(Real) cot
Given a real number x that is not a multiple of π, returns cot(x).
cot(Real) log
Given a positive real number x, returns log(x).
log(Real) New function
You are allow to create new functions. The syntax is different as usual. On the left-hand side of the equal sign, the name of the function and its variables need to be specified. On the right-hand side, the expression of the function. Note the assignation without evaluating symbol :=, instead of the usual assign and evaluating =.
Examples:
g(x):= x+3
f(x):= integral(x+3)+integral(x)
h(x,y,z):= x+y+zcosh
Given a number x, returns cosh(x). Returns a number in the interval [1,+∞).
cosh(Real) sinh
Given a number x, returns sinh(x).
sinh(Real) tanh
Given a number x, returns tanh(x). Returns a number in the interval (-1,1).
tanh(Real) arcosh
Given a real number in the interval [1,+∞), returns the number whose hyperbolic cosine is x. Returns a number in the interval [0,+∞].
arcosh(Real) arsinh
Given a real number x, returns the number whose hyperbolic sine is x.
arsinh(Real) artanh
Given a number x in the interval (-1,1), returns the number whose hyperbolic tangent is x.
artanh(Real) ln
Given a positive real number x, returns ln(x).
artanh(Real) root
Given a real number x and a natural n, computes 
.
root(Natural, Real) sec
Given a real number that is not an odd multiple of 
, returns sec(x). Returns a number in the interval (-∞,-1]∪[1,+∞).
sec(Real) sin
Given a number x, returns sin(x). Returns a number in the interval [-1,1].
sin(Real) sqrt
Given a real number, returns its square root.
sqrt(Real) tan
Given a real number that is not an odd multiple of 
, returns tan(x).
tan(Real)