COS

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

• _PI (QB64 function)
• SIN (sine)
• ATN (arctangent)
• TAN (tangent)
• Mathematical Operations
• Derived Mathematical Functions

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