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114 lines
2.9 KiB
Markdown
114 lines
2.9 KiB
Markdown
The [COS](COS) function returns the horizontal component or the cosine of an angle measured in radians.
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## Syntax
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> value! = [COS](COS)(radianAngle!)
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## Parameter(s)
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* The radianAngle! must be measured in radians.
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## Description
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* To convert from degrees to radians, multiply degrees * π / 180.
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* [COS](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](SINGLE) or [DOUBLE](DOUBLE) precision depending on its argument.
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> COS(4) = -.6536436 ...... COS(4#) = -.6536436208636119
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## Example(s)
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Converting degree angles to radians for QBasic's trig functions and drawing the line at the angle.
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```vb
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SCREEN 12
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PI = 4 * ATN(1)
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PRINT "PI = 4 * ATN(1) ="; PI
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PRINT "COS(PI) = "; COS(PI)
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PRINT "SIN(PI) = "; SIN(PI)
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DO
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PRINT
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INPUT "Enter the degree angle (0 quits): ", DEGREES%
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RADIANS = DEGREES% * PI / 180
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PRINT "RADIANS = DEGREES% * PI / 180 = "; RADIANS
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PRINT "X = COS(RADIANS) = "; COS(RADIANS)
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PRINT "Y = SIN(RADIANS) = "; SIN(RADIANS)
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CIRCLE (400, 240), 2, 12
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LINE (400, 240)-(400 + (50 * SIN(RADIANS)), 240 + (50 * COS(RADIANS))), 11
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DEGREES% = RADIANS * 180 / PI
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PRINT "DEGREES% = RADIANS * 180 / PI ="; DEGREES%
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LOOP UNTIL DEGREES% = 0
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```
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```text
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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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```
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> *Explanation:* When 8.742278E-08(.00000008742278) is returned by [SIN](SIN) or COS the value is essentially zero.
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Creating 12 analog clock hour points using [CIRCLE](CIRCLE)s and [PAINT](PAINT)
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```vb
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PI2 = 8 * ATN(1) '2 * π
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arc! = PI2 / 12 'arc interval between hour circles
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SCREEN 12
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FOR t! = 0 TO PI2 STEP arc!
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cx% = CINT(COS(t!) * 70) ' pixel columns (circular radius = 70)
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cy% = CINT(SIN(t!) * 70) ' pixel rows
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CIRCLE (cx% + 320, cy% + 240), 3, 12
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PAINT STEP(0, 0), 9, 12
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NEXT
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```
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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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Creating a rotating spiral with COS and [SIN](SIN).
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```vb
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SCREEN _NEWIMAGE(640, 480, 32)
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DO
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LINE (0, 0)-(640, 480), _RGB(0, 0, 0), BF
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j = j + 1
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PSET (320, 240)
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FOR i = 0 TO 100 STEP .1
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LINE -(.05 * i * i * COS(j + i) + 320, .05 * i * i * SIN(j + i) + 240)
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NEXT
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PSET (320, 240)
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FOR i = 0 TO 100 STEP .1
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LINE -(.05 * i * i * COS(j + i + 10) + 320, .05 * i * i * SIN(j + i + 10) + 240)
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NEXT
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PSET (320, 240)
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FOR i = 0 TO 100 STEP .1
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PAINT (.05 * i * i * COS(j + i + 5) + 320, .05 * i * i * SIN(j + i + 5) + 240)
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NEXT
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_DISPLAY
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_LIMIT 30
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LOOP UNTIL INP(&H60) = 1 'escape exit
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```
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## See Also
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* [_PI](_PI) (QB64 function)
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* [SIN](SIN) (sine)
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* [ATN](ATN) (arctangent)
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* [TAN](TAN) (tangent)
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*[Mathematical Operations](Mathematical-Operations)
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* [Mathematical Operations](Mathematical-Operations)
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