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108 lines
3.8 KiB
Plaintext
108 lines
3.8 KiB
Plaintext
The [[COS]] function returns the horizontal component or the cosine of an angle measured in radians.
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{{PageSyntax}}
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: {{Parameter|value!}} = [[COS]]({{Parameter|radianAngle!}})
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{{Parameters}}
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* The {{Parameter|radianAngle!}} must be measured in radians.
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{{PageDescription}}
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* 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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{{PageExamples}}
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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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{{PageSeeAlso}}
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* [[_PI]] {{text|(QB64 function)}}
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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}}
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