Elementary functions¶

Sin(x)

trigonometric sine function

Example

In> Sin(1)
Out> Sin(1);
In> N(Sin(1),20)
Out> 0.84147098480789650665;
In> Sin(Pi/4)
Out> Sqrt(2)/2;

Cos(x)

trigonometric cosine function

Example

In> Cos(1)
Out> Cos(1);
In> N(Cos(1),20)
Out> 0.5403023058681397174;
In> Cos(Pi/4)
Out> Sqrt(1/2);

Tan(x)

trigonometric tangent function

Example

In> Tan(1)
Out> Tan(1);
In> N(Tan(1),20)
Out> 1.5574077246549022305;
In> Tan(Pi/4)
Out> 1;

ArcSin(x)

inverse trigonometric function arc-sine

Example

In> ArcSin(1)
Out> Pi/2;
In> ArcSin(1/3)
Out> ArcSin(1/3);
In> Sin(ArcSin(1/3))
Out> 1/3;
In> x:=N(ArcSin(0.75))
Out> 0.848062;
In> N(Sin(x))
Out> 0.7499999477;

ArcCos(x)

inverse trigonometric function arc-cosine

Example

In> ArcCos(0)
Out> Pi/2
In> ArcCos(1/3)
Out> ArcCos(1/3)
In> Cos(ArcCos(1/3))
Out> 1/3
In> x:=N(ArcCos(0.75))
Out> 0.7227342478
In> N(Cos(x))
Out> 0.75

ArcTan(x)

inverse trigonometric function arc-tangent

Example

In> ArcTan(1)
Out> Pi/4
In> ArcTan(1/3)
Out> ArcTan(1/3)
In> Tan(ArcTan(1/3))
Out> 1/3
In> x:=N(ArcTan(0.75))
Out> 0.643501108793285592213351264945231378078460693359375
In> N(Tan(x))
Out> 0.75

Exp(x)

exponential function

Example

In> Exp(0)
Out> 1;
In> Exp(I*Pi)
Out> -1;
In> N(Exp(1))
Out> 2.7182818284;

Ln(x)

natural logarithm

Example

In> Ln(1)
Out> 0;
In> Ln(Exp(x))
Out> x;
In> D(x) Ln(x)
Out> 1/x;


Exp(), Arg()

Sqrt(x)

square root

Example

In> Sqrt(16)
Out> 4;
In> Sqrt(15)
Out> Sqrt(15);
In> N(Sqrt(15))
Out> 3.8729833462;
In> Sqrt(4/9)
Out> 2/3;
In> Sqrt(-1)
Out> Complex(0,1);


Abs(x)

absolute value or modulus of complex number

Example

In> Abs(2);
Out> 2;
In> Abs(-1/2);
Out> 1/2;
In> Abs(3+4*I);
Out> 5;


Sign(), Arg()

Sign(x)

sign of a number

Example

In> Sign(2)
Out> 1;
In> Sign(-3)
Out> -1;
In> Sign(0)
Out> 1;
In> Sign(-3) * Abs(-3)
Out> -3;


Arg(), Abs()