COS: Difference between revisions

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(Created page with "The COS function returns the horizontal component or the cosine of an angle measured in radians. {{PageSyntax}} : {{Parameter|value!}} = COS({{Parameter|radianAngle!}}) {{Parameters}} * The {{Parameter|radianAngle!}} must be measured in radians. {{PageDescription}} * To convert from degrees to radians, multiply degrees * π / 180. * COSINE is the horizontal component of a unit vector in the direction theta (θ). * COS(x) can be calculated in ei...")
 
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{{PageSyntax}}  
{{PageSyntax}}
: {{Parameter|value!}} = [[COS]]({{Parameter|radianAngle!}})
: {{Parameter|value!}} = [[COS]]({{Parameter|radianAngle!}})




{{Parameters}}
{{PageParameters}}
* The {{Parameter|radianAngle!}} must be measured in radians.  
* The {{Parameter|radianAngle!}} must be measured in radians.




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* To convert from degrees to radians, multiply degrees * π / 180.
* To convert from degrees to radians, multiply degrees * π / 180.
* [[COS]]INE is the horizontal component of a unit vector in the direction theta (θ).
* [[COS]]INE is the horizontal component of a unit vector in the direction theta (θ).
* COS(x) can be calculated in either [[SINGLE]] or [[DOUBLE]] precision depending on its argument.
* COS(x) can be calculated in either [[SINGLE]] or [[DOUBLE]] precision depending on its argument.
::: COS(4) = -.6536436 ...... COS(4#) = -.6536436208636119
::: COS(4) = -.6536436 ...... COS(4#) = -.6536436208636119


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{{PageExamples}}
{{PageExamples}}
''Example 1:'' Converting degree angles to radians for QBasic's trig functions and drawing the line at the angle.
''Example 1:'' Converting degree angles to radians for QBasic's trig functions and drawing the line at the angle.
{{CodeStart}} '' ''
{{CodeStart}}
{{Cl|SCREEN}} 12
{{Cl|SCREEN}} 12
PI = 4 * {{Cl|ATN}}(1)
PI = 4 * {{Cl|ATN}}(1)
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   DEGREES% = RADIANS * 180 / PI
   DEGREES% = RADIANS * 180 / PI
   {{Cl|PRINT}} "DEGREES% = RADIANS * 180 / PI ="; DEGREES%
   {{Cl|PRINT}} "DEGREES% = RADIANS * 180 / PI ="; DEGREES%
{{Cl|LOOP}} {{Cl|UNTIL}} DEGREES% = 0 '' ''
{{Cl|LOOP}} {{Cl|UNTIL}} DEGREES% = 0
{{CodeEnd}}
{{CodeEnd}}
{{OutputStart}}
{{OutputStart}}
Line 53: Line 53:


''Example 2:'' Creating 12 analog clock hour points using [[CIRCLE]]s and [[PAINT]]
''Example 2:'' Creating 12 analog clock hour points using [[CIRCLE]]s and [[PAINT]]
{{CodeStart}} '' ''
{{CodeStart}}
  PI2 = 8 * {{Cl|ATN}}(1)                  '2 * π
  PI2 = 8 * {{Cl|ATN}}(1)                  '2 * π
  arc! = PI2 / 12                          'arc interval between hour circles
  arc! = PI2 / 12                          'arc interval between hour circles
  {{Cl|SCREEN (statement)|SCREEN}} 12
  {{Cl|SCREEN}} 12
  FOR t! = 0 TO PI2 STEP arc!
  FOR t! = 0 TO PI2 STEP arc!
   cx% = {{Cl|CINT}}({{Cl|COS}}(t!) * 70) ' pixel columns (circular radius = 70)
   cx% = {{Cl|CINT}}({{Cl|COS}}(t!) * 70) ' pixel columns (circular radius = 70)
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   {{Cl|CIRCLE}} (cx% + 320, cy% + 240), 3, 12
   {{Cl|CIRCLE}} (cx% + 320, cy% + 240), 3, 12
   {{Cl|PAINT}} {{Cl|STEP}}(0, 0), 9, 12
   {{Cl|PAINT}} {{Cl|STEP}}(0, 0), 9, 12
  NEXT '' ''
  NEXT
{{CodeEnd}}
{{CodeEnd}}
{{small|Code by Ted Weissgerber}}
{{Small|Code by Ted Weissgerber}}
''Explanation:'' The 12 circles are placed at radian angles that are 1/12 of 6.28318 or .523598 radians apart.
''Explanation:'' The 12 circles are placed at radian angles that are 1/12 of 6.28318 or .523598 radians apart.




''Example 3:'' Creating a rotating spiral with COS and [[SIN]].
''Example 3:'' Creating a rotating spiral with COS and [[SIN]].
{{CodeStart}} '' ''
{{CodeStart}}
{{Cl|SCREEN}} {{Cl|_NEWIMAGE}}(640, 480, 32)
{{Cl|SCREEN}} {{Cl|_NEWIMAGE}}(640, 480, 32)


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   {{Cl|_DISPLAY}}
   {{Cl|_DISPLAY}}
   {{Cl|_LIMIT}} 30
   {{Cl|_LIMIT}} 30
{{Cl|LOOP}} {{Cl|UNTIL}} {{Cl|INP}}({{Cl|&H}}60) = 1 'escape exit '' ''
{{Cl|LOOP}} {{Cl|UNTIL}} {{Cl|INP}}({{Cl|&H}}60) = 1 'escape exit
{{CodeEnd}}
{{CodeEnd}}
{{small|Code by Ben}}
{{Small|Code by Ben}}
 


{{PageSeeAlso}}
{{PageSeeAlso}}
* [[_PI]] {{text|(QB64 function)}}
* [[_PI]] {{Text|(QB64 function)}}
* [[SIN]] {{text|(sine)}}
* [[SIN]] {{Text|(sine)}}
* [[ATN]] {{text|(arctangent)}}
* [[ATN]] {{Text|(arctangent)}}
* [[TAN]] {{text|(tangent)}}
* [[TAN]] {{Text|(tangent)}}
*[[Mathematical Operations]]
*[[Mathematical Operations]]
*[[Mathematical_Operations#Derived_Mathematical_Functions|Derived Mathematical Functions]]
*[[Mathematical Operations#Derived_Mathematical_Functions|Derived Mathematical Functions]]




{{PageNavigation}}
{{PageNavigation}}

Latest revision as of 22:20, 11 February 2023

The COS function returns the horizontal component or the cosine of an angle measured in radians.


Syntax

value! = COS(radianAngle!)


Parameters

  • The radianAngle! must be measured in radians.


Description

  • To convert from degrees to radians, multiply degrees * π / 180.
  • COSINE is the horizontal component of a unit vector in the direction theta (θ).
  • COS(x) can be calculated in either SINGLE or DOUBLE precision depending on its argument.
COS(4) = -.6536436 ...... COS(4#) = -.6536436208636119


Examples

Example 1: Converting degree angles to radians for QBasic's trig functions and drawing the line at the angle. 

SCREEN 12
PI = 4 * ATN(1)
PRINT "PI = 4 * ATN(1) ="; PI
PRINT "COS(PI) = "; COS(PI)
PRINT "SIN(PI) = "; SIN(PI)
DO
  PRINT
  INPUT "Enter the degree angle (0 quits): ", DEGREES%
  RADIANS = DEGREES% * PI / 180
  PRINT "RADIANS = DEGREES% * PI / 180 = "; RADIANS
  PRINT "X = COS(RADIANS) = "; COS(RADIANS)
  PRINT "Y = SIN(RADIANS) = "; SIN(RADIANS)
  CIRCLE (400, 240), 2, 12
  LINE (400, 240)-(400 + (50 * SIN(RADIANS)), 240 + (50 * COS(RADIANS))), 11
  DEGREES% = RADIANS * 180 / PI
  PRINT "DEGREES% = RADIANS * 180 / PI ="; DEGREES%
LOOP UNTIL DEGREES% = 0

PI = 4 * ATN(1) = 3.141593
COS(PI) = -1
SIN(PI) = -8.742278E-08

Enter the degree angle (0 quits): 45
RADIANS = DEGREES% * PI / 180 = .7853982
X = COS(RADIANS) = .7071068
Y = SIN(RADIANS) = .7071068
DEGREES% = RADIANS * 180 / PI = 45
Explanation: When 8.742278E-08(.00000008742278) is returned by SIN or COS the value is essentially zero.


Example 2: Creating 12 analog clock hour points using CIRCLEs and PAINT 

 PI2 = 8 * ATN(1)                  '2 * π
 arc! = PI2 / 12                          'arc interval between hour circles
 SCREEN 12
 FOR t! = 0 TO PI2 STEP arc!
   cx% = CINT(COS(t!) * 70) ' pixel columns (circular radius = 70)
   cy% = CINT(SIN(t!) * 70) ' pixel rows
   CIRCLE (cx% + 320, cy% + 240), 3, 12
   PAINT STEP(0, 0), 9, 12
 NEXT
Code by Ted Weissgerber

Explanation: The 12 circles are placed at radian angles that are 1/12 of 6.28318 or .523598 radians apart.


Example 3: Creating a rotating spiral with COS and SIN. 

SCREEN _NEWIMAGE(640, 480, 32)

DO
  LINE (0, 0)-(640, 480), _RGB(0, 0, 0), BF
  j = j + 1
  PSET (320, 240)
  FOR i = 0 TO 100 STEP .1
    LINE -(.05 * i * i * COS(j + i) + 320, .05 * i * i * SIN(j + i) + 240)
  NEXT
  PSET (320, 240)
  FOR i = 0 TO 100 STEP .1
    LINE -(.05 * i * i * COS(j + i + 10) + 320, .05 * i * i * SIN(j + i + 10) + 240)
  NEXT
  PSET (320, 240)
  FOR i = 0 TO 100 STEP .1
    PAINT (.05 * i * i * COS(j + i + 5) + 320, .05 * i * i * SIN(j + i + 5) + 240)
  NEXT

  _DISPLAY
  _LIMIT 30
LOOP UNTIL INP(&H60) = 1 'escape exit
Code by Ben


See also


Navigation:
Main Page with Articles and Tutorials
Keyword Reference - Alphabetical
Keyword Reference - By usage
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