mirror of
https://github.com/QB64-Phoenix-Edition/QB64pe.git
synced 2024-07-26 16:45:53 +00:00
6e01fc8dce
Added new _STRCMP and _STRICMP commands for quick string comparisons. Cleaned up QB64 to finish removing the QUI (quick user insert) code and folders. Altered UCASE and LCASE routines to be faster in some situations for us.
100 lines
3.7 KiB
Plaintext
100 lines
3.7 KiB
Plaintext
The '''COS''' function returns the cosine of an angle measured in radians.
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::::::''Syntax:'' value! = COS(''radian_angle!'')
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* The ''radian_angle'' must be measured in radians. To convert from degrees to radians, multiply degrees * π/180.
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* [[COS]]INE is the horizontal component of a unit vector in the direction theta (θ).
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* COS(x) can be calculated in either [[SINGLE]] or [[DOUBLE]] precision depending on its argument.
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::: COS(4) = -.6536436 ...... COS(4#) = -.6536436208636119
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''Example 1:'' Converting degree angles to radians for Qbasic's trig functions and drawing the line at the angle.
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{{CodeStart}} '' ''
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{{Cl|SCREEN}} 12
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PI = 4 * {{Cl|ATN}}(1)
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{{Cl|PRINT}} "PI = 4 * {{Cl|ATN}}(1) ="; PI
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{{Cl|PRINT}} "COS(PI) = "; {{Cl|COS}}(PI)
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{{Cl|PRINT}} "SIN(PI) = "; {{Cl|SIN}}(PI)
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{{Cl|DO...LOOP|DO}}
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{{Cl|PRINT}}
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{{Cl|INPUT}} "Enter the degree angle (0 quits): ", DEGREES%
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RADIANS = DEGREES% * PI / 180
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{{Cl|PRINT}} "RADIANS = DEGREES% * PI / 180 = "; RADIANS
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{{Cl|PRINT}} "X = COS(RADIANS) = "; {{Cl|COS}}(RADIANS)
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{{Cl|PRINT}} "Y = SIN(RADIANS) = "; {{Cl|SIN}}(RADIANS)
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{{Cl|CIRCLE}} (400, 240), 2, 12
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{{Cl|LINE}} (400, 240)-(400 + (50 * {{Cl|SIN}}(RADIANS)), 240 + (50 * {{Cl|COS}}(RADIANS))), 11
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DEGREES% = RADIANS * 180 / PI
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{{Cl|PRINT}} "DEGREES% = RADIANS * 180 / PI ="; DEGREES%
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{{Cl|LOOP}} {{Cl|UNTIL}} DEGREES% = 0 '' ''
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{{CodeEnd}}
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{{OutputStart}}
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PI = 4 * ATN(1) = 3.141593
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COS(PI) = -1
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SIN(PI) = -8.742278E-08
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Enter the degree angle (0 quits): 45
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RADIANS = DEGREES% * PI / 180 = .7853982
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X = COS(RADIANS) = .7071068
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Y = SIN(RADIANS) = .7071068
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DEGREES% = RADIANS * 180 / PI = 45
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{{OutputEnd}}
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: ''Explanation:'' When 8.742278E-08(.00000008742278) is returned by [[SIN]] or COS the value is essentially zero.
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''Example 2:'' Creating 12 analog clock hour points using [[CIRCLE]]s and [[PAINT]]
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{{CodeStart}} '' ''
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PI2 = 8 * {{Cl|ATN}}(1) '2 * π
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arc! = PI2 / 12 'arc interval between hour circles
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{{Cl|SCREEN (statement)|SCREEN}} 12
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FOR t! = 0 TO PI2 STEP arc!
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cx% = {{Cl|CINT}}({{Cl|COS}}(t!) * 70) ' pixel columns (circular radius = 70)
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cy% = {{Cl|CINT}}({{Cl|SIN}}(t!) * 70) ' pixel rows
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{{Cl|CIRCLE}} (cx% + 320, cy% + 240), 3, 12
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{{Cl|PAINT}} {{Cl|STEP}}(0, 0), 9, 12
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NEXT '' ''
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{{CodeEnd}}
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{{small|Code by Ted Weissgerber}}
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''Explanation:'' The 12 circles are placed at radian angles that are 1/12 of 6.28318 or .523598 radians apart.
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''Example 3:'' Creating a rotating spiral with COS and [[SIN]].
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{{CodeStart}} '' ''
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{{Cl|SCREEN}} {{Cl|_NEWIMAGE}}(640, 480, 32)
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{{Cl|DO...LOOP|DO}}
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{{Cl|LINE}} (0, 0)-(640, 480), {{Cl|_RGB}}(0, 0, 0), BF
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j = j + 1
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{{Cl|PSET}} (320, 240)
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{{Cl|FOR...NEXT|FOR}} i = 0 {{Cl|TO}} 100 {{Cl|STEP}} .1
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{{Cl|LINE}} -(.05 * i * i * {{Cl|COS}}(j + i) + 320, .05 * i * i * {{Cl|SIN}}(j + i) + 240)
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{{Cl|NEXT}}
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{{Cl|PSET}} (320, 240)
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{{Cl|FOR...NEXT|FOR}} i = 0 {{Cl|TO}} 100 {{Cl|STEP}} .1
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{{Cl|LINE}} -(.05 * i * i * {{Cl|COS}}(j + i + 10) + 320, .05 * i * i * {{Cl|SIN}}(j + i + 10) + 240)
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{{Cl|NEXT}}
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{{Cl|PSET}} (320, 240)
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{{Cl|FOR...NEXT|FOR}} i = 0 {{Cl|TO}} 100 {{Cl|STEP}} .1
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{{Cl|PAINT}} (.05 * i * i * {{Cl|COS}}(j + i + 5) + 320, .05 * i * i * {{Cl|SIN}}(j + i + 5) + 240)
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{{Cl|NEXT}}
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{{Cl|_DISPLAY}}
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{{Cl|_LIMIT}} 30
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{{Cl|LOOP}} {{Cl|UNTIL}} {{Cl|INP}}({{Cl|&H}}60) = 1 'escape exit '' ''
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{{CodeEnd}}
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{{small|Code by Ben}}
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''See also:''
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* [[SIN]] {{text|(sine)}}
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* [[ATN]] {{text|(arctangent)}}
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* [[TAN]] {{text|(tangent)}}
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*[[Mathematical Operations]]
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*[[Mathematical_Operations#Derived_Mathematical_Functions|Derived Mathematical Functions]]
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{{PageNavigation}} |