| degrees# = angle in degrees. |
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For angles between 0 and 90 degrees this is defined by the sides of a right triangle. The cosine is the side adjacent to 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 x coordinate of this point is the cosine 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 cosine function repeats every 360 degrees. So Cos(-360), Cos(0), Cos(360), Cos(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 |
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; 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 |