SIN: Difference between revisions

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The {{KW|SIN}} function returns the vertical component or sine of an angle measured in radians.  
The {{KW|SIN}} function returns the vertical component or sine of an angle measured in radians.




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{{Parameters}}
{{Parameters}}
* The ''radian_angle'' must be measured in radians from 0 to 2 * Pi.  
* The ''radian_angle'' must be measured in radians from 0 to 2 * Pi.




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''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}}
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''Example 2:'' Displays rotating gears made using SIN and [[COS]] to place the teeth lines.
''Example 2:'' Displays rotating gears made using SIN and [[COS]] to place the teeth lines.
{{CodeStart}} '' ''
{{CodeStart}}
{{Cl|SCREEN (statement)|SCREEN}} 9
{{Cl|SCREEN (statement)|SCREEN}} 9
{{Cl|DIM}} {{Cl|SHARED}} Pi {{Cl|AS}} {{Cl|SINGLE}}
{{Cl|DIM}} {{Cl|SHARED}} Pi {{Cl|AS}} {{Cl|SINGLE}}
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         {{Cl|CALL}} GEARZ(320 + 57, 140 + 57, 40, 20, 4, G, 14)
         {{Cl|CALL}} GEARZ(320 + 57, 140 + 57, 40, 20, 4, G, 14)
         {{Cl|CALL}} GEARZ(320 + 100, 140 + 100, 20, 10, 4, -G * 2 - 15, 15)
         {{Cl|CALL}} GEARZ(320 + 100, 140 + 100, 20, 10, 4, -G * 2 - 15, 15)
         {{Cl|_DISPLAY}}  
         {{Cl|_DISPLAY}}
         {{Cl|_LIMIT}} 20                'regulates gear speed and CPU usage
         {{Cl|_LIMIT}} 20                'regulates gear speed and CPU usage
     {{Cl|NEXT}} G
     {{Cl|NEXT}} G
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     IF {{Cl|INKEY$}} <> "" THEN {{Cl|END}}
     IF {{Cl|INKEY$}} <> "" THEN {{Cl|END}}
{{Cl|NEXT}} t
{{Cl|NEXT}} t
{{Cl|PAINT}} (XP, YP), CLR            'gear colors optional    
{{Cl|PAINT}} (XP, YP), CLR            'gear colors optional
{{Cl|END SUB}} '' ''
{{Cl|END SUB}}
{{CodeEnd}}
{{CodeEnd}}
{{small|Adapted from code by: DarthWho}}
{{small|Adapted from code by: DarthWho}}
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''Example 3:'' Displaying the current seconds for an analog clock. See [[COS]] for the clock face hour markers.
''Example 3:'' Displaying the current seconds for an analog clock. See [[COS]] for the clock face hour markers.
{{CodeStart}} '' ''
{{CodeStart}}
{{Cl|SCREEN}} 12
{{Cl|SCREEN}} 12
Pi2! = 8 * {{Cl|ATN}}(1): sec! = Pi2! / 60  ' (2 * pi) / 60 movements per rotation  
Pi2! = 8 * {{Cl|ATN}}(1): sec! = Pi2! / 60  ' (2 * pi) / 60 movements per rotation
{{Cl|CIRCLE}} (320, 240), 80, 1
{{Cl|CIRCLE}} (320, 240), 80, 1
{{Cl|DO}}
{{Cl|DO}}
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   Seconds% = {{Cl|VAL}}({{Cl|RIGHT$}}({{Cl|TIME$}}, 2)) - 15 ' update seconds
   Seconds% = {{Cl|VAL}}({{Cl|RIGHT$}}({{Cl|TIME$}}, 2)) - 15 ' update seconds
   S! = Seconds% * sec! ' radian from the TIME$ value
   S! = Seconds% * sec! ' radian from the TIME$ value
   Sx% = {{Cl|CINT}}({{Cl|COS}}(S!) * 60)  ' pixel columns (60 = circular radius)  
   Sx% = {{Cl|CINT}}({{Cl|COS}}(S!) * 60)  ' pixel columns (60 = circular radius)
   Sy% = {{Cl|CINT}}({{Cl|SIN}}(S!) * 60)  ' pixel rows
   Sy% = {{Cl|CINT}}({{Cl|SIN}}(S!) * 60)  ' pixel rows
   {{Cl|LINE}} (320, 240)-(Sx% + 320, Sy% + 240), 12
   {{Cl|LINE}} (320, 240)-(Sx% + 320, Sy% + 240), 12

Revision as of 02:40, 23 January 2023

The Template:KW function returns the vertical component or sine of an angle measured in radians.


Syntax

value! = SIN(radian_angle!)


Template:Parameters

  • The radian_angle must be measured in radians from 0 to 2 * Pi.


Description

  • To convert from degrees to radians, multiply degrees * π/180.
  • SINE is the vertical component of a unit vector in the direction theta (θ).
  • Accuracy can be determined as SINGLE by default or DOUBLE by following the parameter value with a # suffix.


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: Displays rotating gears made using SIN and COS to place the teeth lines. 

SCREEN 9
DIM SHARED Pi AS SINGLE
Pi = 4 * ATN(1)
DO
    FOR G = 0 TO Pi * 2 STEP Pi / 100
        CLS                                   'erase previous
        CALL GEARZ(160, 60, 40, 20, 4, G, 10)
        CALL GEARZ(240, 60, 40, 20, 4, -G, 11)
        CALL GEARZ(240, 140, 40, 20, 4, G, 12)
        CALL GEARZ(320, 140, 40, 20, 4, -G, 13)
        CALL GEARZ(320 + 57, 140 + 57, 40, 20, 4, G, 14)
        CALL GEARZ(320 + 100, 140 + 100, 20, 10, 4, -G * 2 - 15, 15)
        _DISPLAY
        _LIMIT 20                 'regulates gear speed and CPU usage
    NEXT G
LOOP UNTIL INKEY$ <> ""
END

SUB GEARZ (XP, YP, RAD, Teeth, TH, G, CLR)
t = 0
x = XP + (RAD + TH * SIN(0)) * COS(0)
y = YP + (RAD + TH * SIN(0)) * SIN(0)
PRESET (x, y)
m = Teeth * G
FOR t = -Pi / 70 TO 2 * Pi STEP Pi / 70
    x = XP + (RAD + TH * SIN((Teeth * t + m)) ^ 3) * COS(t)
    y = YP + (RAD + TH * SIN((Teeth * t + m)) ^ 3) * SIN(t)
    LINE -(x, y), CLR
    IF INKEY$ <> "" THEN END
NEXT t
PAINT (XP, YP), CLR            'gear colors optional
END SUB
Adapted from code by: DarthWho


Example 3: Displaying the current seconds for an analog clock. See COS for the clock face hour markers. 

SCREEN 12
Pi2! = 8 * ATN(1): sec! = Pi2! / 60  ' (2 * pi) / 60 movements per rotation
CIRCLE (320, 240), 80, 1
DO
  LOCATE 1, 1: PRINT TIME$
  Seconds% = VAL(RIGHT$(TIME$, 2)) - 15 ' update seconds
  S! = Seconds% * sec! ' radian from the TIME$ value
  Sx% = CINT(COS(S!) * 60)   ' pixel columns (60 = circular radius)
  Sy% = CINT(SIN(S!) * 60)   ' pixel rows
  LINE (320, 240)-(Sx% + 320, Sy% + 240), 12
  DO: Check% = VAL(RIGHT$(TIME$, 2)) - 15: LOOP UNTIL Check% <> Seconds%  ' wait loop
  LINE (320, 240)-(Sx% + 320, Sy% + 240), 0 ' erase previous line
LOOP UNTIL INKEY$ = CHR$(27) ' escape keypress exits
Code by: Ted Weissgerber

The value of 2 π is used to determine the sec! multiplier that determines the radian value as S! The value is divided by 60 second movements. To calculate the seconds the TIME$ function is used and that value is subtracted 15 seconds because the 0 value of pi is actually the 3 hour of the clock (15 seconds fast). SIN and COS will work with negative values the same as positive ones! Then the column and row coordinates for one end of the line are determined using SIN and COS multiplied by the radius of the circular line movements. The minute and hour hands could use similar procedures to read different parts of TIME$.


See also


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