# Sin# ( degrees# )

# Parameters

degrees# = angle in degrees.

# Description

Sine of an angle. The angle is measured in degrees.
For angles between 0 and 90 degrees this is defined by the sides of a right triangle. The sine is the side opposite the angle divided by the hypotenuse.
Outside of 0 to 90 the definition uses a circle with radius=1. The angle is placed at the center of the circle, with one side on the positive x-axis. The other side hits the circle at some point. The y coordinate of this point is the sine of the angle.
The positive y-axis corresonds to +90 degrees. This is a common source of confusion in Blitz. With screen coordinates ( pixels ) the y-axis points downward. But in the 3d world the y-axis typically points upward.
Another possible snag is the size of the angle. In principle, the sine function repeats every 360 degrees. So Sin(-360), Sin(0), Sin(360), Sin(720) etc. should all be exactly the same. But in practice the accuracy decreases as the angle gets farther away from zero.
See also ASin, Cos, ACos, Tan, Atan, ATan2

# Example

; Sin / Cos / Tan example.
; Left/Right arrow keys change angle. Escape quits.
Const width = 640, height = 480
Const radius# = .2 * height
Const KEY_ESC = 1, KEY_LEFT = 203, KEY_RIGHT = 205
Graphics width, height
SetBuffer BackBuffer( )
Origin width / 3, height / 2
angle# = 0.0
While Not KeyDown( KEY_ESC )
; NOTE: It is usually best to avoid very large angles.
; The 'If angle...' lines show one way to do this.
; Mod is another possibility.
If KeyDown( KEY_LEFT ) Then angle = angle - .5
; If angle < 0.0 Then angle = angle + 360
If KeyDown( KEY_RIGHT ) Then angle = angle + .5
; If angle >= 360.0 Then angle = angle - 360
Cls
Color 80, 80, 0 ; pale yellow circle
Oval -radius, -radius, 2 * radius, 2 * radius, False
For a# = 0.0 To Abs( angle Mod 360 ) Step .5
x# = radius * Cos( a ) ; (x,y) is a point on the circle
y# = radius * Sin( a ) ; corresponding to angle a.
If ( angle Mod 360 < 0 ) Then y = -y ; reverse for negative angle
WritePixel x, y, $ffff00 ; bright yellow
Next
Color 255, 255, 0 ; yellow
Line 0, 0, radius * Cos( angle ), radius * Sin( angle )
Color 0, 255, 0 ; green
Line 0, 0, radius * Cos( angle ), 0
Text radius * 1.5, 10, "Cos( angle ) = " + Cos( angle )
Color 255, 0, 0 ; red
Line radius * Cos( angle ), 0, radius * Cos( angle ), radius * Sin( angle )
Text radius * 1.5, -10, "Sin( angle ) = " + Sin( angle )
Color 255, 255, 255
Text radius * 1.5, -30, " angle = " + angle
Text radius * 1.5, 30, "Tan( angle ) = " + Tan( angle )
Flip
Wend
End

Index
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