Matematika

paket "matematika";

The matematika package comes with various mathematical functions and constants. Below is a comprehensive list.

Variables:

1. pi
2. e
3. beskonacno
4. minusBeskonacno

Functions:

1. apsolutnaVrijednost
2. arccos
3. arcsin
4. sin
5. cos
6. tg
7. arctg
8. korijen
9. eNa
10. ln
11. log
12. log10
13. log2
14. max
15. min
16. zaokruzi
17. kubniKorijen
18. uStepenima

Variables

Constant pi

Pi is the mathematical constant that represents the ratio of a circle’s circumference to its diameter.

ispis(pi);

Output:

3.141592653589793

Constant e

e is the mathematical constant known as Euler’s number. It is the base of the natural logarithm.

ispis(e);

Output:

2.718281828459045

Infinity

Bosscript has separate constants for positive and negative infinity.

ispis(beskonacno);
ispis(minusBeskonacno);

ispis(apsolutnaVrijednost(22));

ispis(apsolutnaVrijednost(-22));

ispis(apsolutnaVrijednost(0));

Output:

22
22
0

arccos

The arccos function returns the arc cosine of a provided broj.

• takes: x - broj
• returns: an angle in the range from 0.0 to PI radians (broj)
• special cases
  • returns NaN if x is greater than 1 or lower than -1

ispis(arccos(1));

ispis(arccos(0));

ispis(arccos(100));

Output:

0
1.5707963267948966 "comment">// π/2
NaN

arcsin

The arcsin function returns the arc sine of a provided broj.

• takes: x - broj
• returns: an angle in the range from -PI/2 to PI/2 radians (broj)
• special cases
  • returns NaN if x is greater than 1 or lower than -1

ispis(arcsin(0));

ispis(arcsin(1));

ispis(arcsin(100));

Output:

0
1.5707963267948966 "comment">// π/2
NaN

sin

The sin function returns the sine of a provided broj.

• takes: x - angle expressed in degrees (broj)
• returns: sine of the provided angle (broj)
• special cases
  • returns NaN if x is NaN or Infinity

ispis(sin(90));

ispis(sin(0));

ispis(sin(45));

Output:

1
0
0.7071067811865475

cos

The cos function returns the cosine of a provided broj.

• takes: x - angle expressed in degrees (broj)
• returns: cosine of the provided angle (broj)
• special cases
  • returns NaN if x is NaN or Infinity

ispis(cos(90));

ispis(cos(0));

ispis(cos(45));

Output:

0
1
0.7071067811865476

tg

The tg function returns the tangent of a provided broj.

• takes: x - angle expressed in degrees (broj)
• returns: sine of the provided angle (broj)
• special cases
  • returns NaN if x is NaN or Infinity

ispis(tg(90));

ispis(tg(0));

ispis(tg(45));

Output:

1.633123935319537E16 "comment">// Actually undefined
0
1

arctg

The arctg function returns the arc tangent of a provided broj.

• takes: x - broj
• returns: an angle in the range from -PI/2 to PI/2 radians (broj)
• special cases
  • returns NaN if x is NaN

ispis(arctg(0));

ispis(arctg(1));

ispis(arctg(100));

Output:

0
0.7853981633974483
1.5607966601082315

korijen

The korijen function returns the square root of a provided broj.

• takes: x - broj
• returns: square root of provided number (broj)
• special cases:
  • throws Exception if x is a negative number

ispis(korijen(144));

ispis(korijen(2));

ispis(korijen(0));

Output:

12
1.4142135623730951
0

ispis(korijen(-1));

Error: Square root cannot be calculated for negative numbers. Value -1 is invalid.

eNa

The eNa function returns Euler’s number e raised to the power of the provided broj

• takes: x - broj
• returns: e^x (broj)
• special cases:
  • when x is NaN, returns NaN
  • when x is Infinity, returns Infinity
  • when x is -Infinity, returns 0

ispis(eNa(2));

ispis(eNa(-1));

ispis(eNa(0));

Output:

7.38905609893065
0.36787944117144233
1

ln

The ln function returns the natural logarithm of the provided broj.

• takes: x - broj
• returns: natural log of x (broj)
• special cases:
  • throws Exception when x < 0.0
  • ln(NaN) is NaN
  • ln(Infinity) is Infinity
  • ln(0.0) is -Infinity

ispis(ln(14));

ispis(ln(32));

ispis(ln(e));

Output:

2.6390573296152584
3.4657359027997265
1

ispis(ln(-1));

Error: Cannot calculate ln of -1.0: Value must be a positive number

log

The log function computes the logarithm of the value x to the given base b.

• takes: x - number (broj), b - base (broj)
• returns: log base b of x
• special cases:
  • log(x, b) is NaN if either x or b are NaN
  • log(x, b) is NaN when x < 0 or b <= 0 or b == 1.0
  • log(Infinity, Infinity) is NaN
  • log(Infinity, b) is Infinity for b > 1 and -Infinity for b < 1
  • log(0.0, b) is -Infinity for b > 1 and Infinity for b > 1

ispis(log(45, 4));

ispis(log(45, 2));

ispis(log(45, 5));

ispis(log(45, 1));

Output:

2.7459265481648374
5.491853096329675
2.3652123889719707
NaN

log10

The log10 function computes the common logarithm (base 10) of the provided broj.

• takes: x - number (broj)
• returns: log base 10 of x
• special cases:
  • returns NaN if x is a negative number

ispis(log10(142));

ispis(log10(12));

ispis(log10(-50));

Output:

2.1522883443830563
1.0791812460476249
NaN

log2

The log2 function computes the binary logarithm (base 2) of the provided broj.

• takes: x - number (broj)
• returns: log base 2 of x
• special cases:
  • returns NaN if x is a negative number

ispis(log2(142));

ispis(log2(12));

ispis(log2(-50));

Output:

7.149747119504682
3.5849625007211565
NaN

max

The max function returns the greater of the two provided broj values.

• takes: x (broj), y (broj)
• returns: the greater of x and y
• special cases:
  • returns NaN if either x or y is NaN

ispis(max(2, 3));

ispis(max(2, -3));

ispis(max(1, 1));

Output:

33
2
1

min

The min function returns the smaller of the two provided broj values.

• takes: x (broj), y (broj)
• returns: the smaller of x and y
• special cases:
  • returns NaN if either x or y is NaN

ispis(min(2, 33));

ispis(min(-2, 33));

ispis(min(2, 2));

Output:

2
-2
2

zaokruzi

The zaokruzi function rounds the given value x towards the closest integer with ties rounded towards even integer.

• takes: x - number (broj)
• returns: x rounded to the closest integer
• special cases:
  • returns x when x is NaN, Infinity, or already an Integer

ispis(zaokruzi(33.33333333));

ispis(zaokruzi(1.25));

ispis(zaokruzi(3.55));

Output:

33
1
4

kubniKorijen

The kubniKorijen function returns the cubic root of a provided broj.

• takes: x - broj
• returns: cubic root of provided number (broj)
• special cases:
  • If x is NaN, then the result is NaN.
  • If x is Infinity, then the result is Infinity

ispis(kubniKorijen(144));

ispis(kubniKorijen(2));

ispis(kubniKorijen(0));

Output:

5.241482788417793
1.2599210498948732
0

uStepenima

The uStepenima function converts an angle measured in radians to an approximately equivalent angle measured in degrees.

• takes: x - angle expressed in radians broj
• returns: x expressed in degrees (broj)
• special cases: none

"comment">// Convert π/2 radians to degrees
ispis(uStepenima(1.5707963267948966));

Output:

90