Q(uick)BASIC Function: COS

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COS Function

A math function that returns the cosine of an angle given in radians

Worth knowing

Useful and cross-version information about the programming environments of QBasic and QuickBasic.

Syntax

ATN(numeric-expression)
COS(angle)
SIN(angle)
TAN(angle)

Description/Parameter(s)

numeric-expression	The ratio between the sides of a right triangle.
angle	An angle expressed in radians.

The ATN function returns an angle in radians.

To convert from degrees to radians, multiply degrees by (PI / 180).

Example

CONST PI=3.141592654
PRINT ATN(TAN(PI/4.0)), PI/4.0    'Output is:  .7853981635  .7853981635
PRINT (COS(180 * (PI / 180)))     'Output is:  -1
PRINT (SIN(90 * (PI / 180)))      'Output is:  1
PRINT (TAN(45 * (PI / 180)))      'Output is:  1.000000000205103

Syntax

COS(numeric-expression)

Description/Parameter(s)

The expression, numeric-expression, can be any numeric type.

By default, the cosine is calculated in single precision. If numeric- expression is a double-precision value, the cosine is calculated in double precision.

You can convert an angle measurement from degrees to radians by multiplying the degrees by ã/180, where ã = 3.141593.

To convert a radian value to degrees, multiply it by 57.2958.

Example

The following program plots the graph of the polar equation r = né for values of n from 0.1-1.1. This program uses the conversion factors x = cos(0) and y = sin(0) to change polar coordinates to Cartesian x,y coordinates. The figure plotted is sometimes known as the Spiral of Archimedes.

CONST PI = 3.141593
'Gray background.
SCREEN 1 : COLOR 7
'Define window large enough for biggest spiral.
WINDOW (-4,-6)-(8,2)
'Draw line from origin to the right.
LINE (0,0)-(2.2*PI,0),1
'Draw ten spirals.
FOR N = 1.1 TO .1 STEP -.1
   'Plot starting point.
   PSET (0,0)
   FOR Angle = 0 TO 2*PI STEP .04
      'Polar equation for spiral.
      R = N * Angle
      'Convert polar coordinates to Cartesian coordinates.
      X = R * COS(Angle)
      Y = R * SIN(Angle)
      'Draw line from previous point to new point.
      LINE -(X,Y),1
   NEXT
NEXT

Syntax

COS(x)

Description/Parameter(s)

The argument x can be of any numeric type.

Usage Notes

The cosine of an angle in a right triangle is the ratio between the length of the side adjacent to the angle and the length of the hypotenuse.
COS is calculated in single precision if the argument x is an integer or single-precision value. If you use any other numeric data type, COS is calculated in double-precision.
To convert values from degrees to radians, multiply the angle (in degrees) times PI/180 (or .0174532925199433) where PI = 3.141593.
To convert a radian value to degrees, multiply it by 180/PI (or 57.2957795130824) where PI = 3.141593.

Example

This program uses the COS function to plot the graph of the polar equation r = n * é for ten values of n from 1.1 to 0.1. The program uses the transformations x = r * cos(é) and y = r * sin(é) to change polar coordinates (r, é) to Cartesian coordinates (x, y). The figure plotted is sometimes known as the Spiral of Archimedes.

CONST PI = 3.141593
'Gray background.
SCREEN 1: COLOR 7
'Define window large enough for biggest spiral.
WINDOW (-4, -6)-(8, 2)
'Draw line from origin to the right.
LINE (0, 0)-(2.2 * PI, 0), 1
'Draw ten spirals.
FOR N = 1.1 TO .1 STEP -.1
   'Plot starting point.
   PSET (0, 0)
   FOR Angle = 0 TO 2 * PI STEP .04
      'Polar equation for spiral.
      R = N * Angle
      'Convert polar coordinates to Cartesian coordinates.
      X = R * COS(Angle)
      Y = R * SIN(Angle)
      'Draw line from previous point to new point.
      LINE -(X, Y), 1
   NEXT
NEXT