# SIN

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

## Syntax

- value! =
**SIN(***radian_angle!***)**

- value! =

## 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 * *

*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

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

- _PI (QB64 function)
- COS (cosine)
- ATN (arctangent)
- TAN (tangent)
- Mathematical Operations
- Derived Mathematical Functions

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