COS
f = COS (x)
Cosine of x
. x
is in radians.
Example 1
cos(0.5)
a = print a ' Output: 0.87758256189037
acos(a)
b = print b ' Output: 0.5
Example 2
'TRIG lesson one.bas SmallBASIC 0.12.2 [B+=MGA] 2016-03-12
'note: the lines in the diagram have been thickened to help see and identify the color
const green=rgb(0,128,0) 'never liked QB color for green
sub drawTRIGtri
'3 points make a triangle, one point requires an x,y coordinate
xmax-100-.25*ymax : yp1=ymax-100 'bottom left angle of triangle
xp1=xmax-100 : yp2=ymax-100 'bottom right corner with right angle
xp2=xmax-100 : yp3=ymax-100-.433*ymax 'upper corner
xp3='green botton line is called side adjacent the yellow angle at the base of this triangle (not the 90 degree right angle)
line xp1,yp1,xp2,yp2,green
line xp1-1,yp1+1,xp2+1,yp2+1,green
line xp1-2,yp1+2,xp2+2,yp2+2,green
'blue vertical line is call side opposite the yellow angle at the base of this triangle (not the 90 degree right angle)
line xp2,yp2,xp3,yp3,9
line xp2+1,yp2+1,xp3+1,yp3-1,9
line xp2+2,yp2+2,xp3+2,yp3-2,9
'red diagonal line always the longest of a right triangle is called the hypotenuse
for i=0 to 6
line xp1,yp1+.5*i,xp3,yp3+i,12
next
'mark the 90 degree angel
rect xp2-50,yp2-50 step 48,48,15
at xp2-50+10,yp2-50+15:?"90"
'the yellow angle: ARC x,y,r, start radians, stop radians[, aspect [, color]] note: start clockwise to stop radians
arc xp1,yp1,.2*ymax/2,2*pi-pi/3,0,1,14
arc xp1,yp1,.18*ymax/2,2*pi-pi/3,0,1,14
'note: here 0 degrees is due east and the angle advances clockwise
end
while 1
cls
drawTRIGtriat 0,0
"A man put up a pole (blue) and attached a 100 foot wire (red)"
?"from top to ground. Now he needs to know the height of the"
?"pole. He doesn't have a ladder nearly that high but he"
?"can use a first lesson in trignometry to get the height of"
?"the pole."
?
?"Trignometry means right triangles. A right triangle is one
?"that contains a 90 degree angle, the same angle a proper
?"pole makes with the ground."
?
?"Trig has made a study of right triangles and made one big
?"discovery: The RATIO of the sides of a right triangle are
?"always the same if the ANGLES of the sides (AKA legs and
?"hypotenuse) are the same."
?"That is trig in a nutshell. Notice I said RATIO of lengths."
?
?"press any when ready...
?pause
cls
drawTRIGtriat 0,0
"The two main RATIOs of Trig are SIN and COS."
?"COS (AKA COSINE) is the RATIO of the green side (next to"
?"the yellow ANGLE) to the hypotenuse (red diagonal) AKA"
?"(adjacent leg) / (hypotenuse) shortened to (adj/hyp)"
?"or here (green line length) / (red line length)."
?"That's it! COS is the leg length next to the angle in"
?"question divided by the diagonal length."
?
?"So the man measures the distance from the pole to where"
?"the wire meets the gound and gets 50 feet. This is the"
?"green leg next to the angle we want to figure out for the"
?"COS RATIO (adj/hyp). In this case it is 50 ft along the"
?"ground divided by 100 ft the diagonal red wire, 50/100=.5"
?"So that means COS of the angle is .5 the man says."
?
?"So the man goes to some trig tables and finds what angle"
?"makes a COS ratio of .5, he is looking up the Arc COS of"
?"the ratio(.5) = the angle whose adj-leg/hypotenuse is .5"
?"Oh! he says that is a 60 degree angle the wire is making"
?"with the ground, the yellow angle is 60 degrees."
?
?"Press any key when ready..."
?Pause
cls
drawTRIGtriat 0,0
"Now that he knows the angle is 60 degrees he can use the"
?"SIN ratio to calculate the height of the pole. The SIN"
?"RATIO is opp/hyp, the (opposite leg length)/(hypotenuse)"
?"The pole/wire = SIN of 60 degrees = .8660"
?"or pole/wire=.866."
?
?"Multiply both sides of this equation by wire length and"
?"get pole=.866*wire."
?"Since the wire is 100, pole = .866*100 = 86.6 feet."
?
?"press any for first screen again..."
?pause
wend
Example 3
At an angle around a given point, SIN and COS and radius (or distance) can locate the absolute screen x,y coordinate.
' Diagrammed SIN and COS.bas SmallBASIC 0.12.2 [B+=MGA] 2016-03-16
' ah finally got diagramed analysis built into single quote commented code!!!
' the color codes match original Trig lesson one
' reminder XMAX, YMAX and PI are built in constants
CONST green =RGB(0,128,0)
' a central point cx,cy around which to draw
XMAX/2:cy=YMAX/2 'again cx,cy can be anywhere on screen so dont make them constant
cx=' highlight center
CIRCLE cx,cy,2,1,15
200 'the radius or distance in pixels from cx,cy desired
r=CIRCLE cx,cy,r,1,8 'we want a point somewhere on this circle, radius = constant distance away from point
' locate point 30 degrees and r distance from cx,cy 30 degrees = PI/6 radians
' here is 30 degrees in tiny purple circle around x=r*cos(rad(30),y=r*sin(rad(30)
CIRCLE cx + r*COS(RAD(30)), cy + r*SIN(RAD(30)), 3, 1, 13 'x,y,r=3,aspect=1,color 13
legendLINE cx,cy,cx+r*COS(RAD(30)),cy,green 'adjacent leg in red
LINE cx+r*COS(RAD(30)),cy,cx+r*COS(RAD(30)),cy + r*SIN(RAD(30)),9 'leg opposite in blue
LINE cx,cy,cx+r*COS(RAD(30)),cy + r*SIN(RAD(30)),12
RECT cx+r*COS(RAD(30))-11,cy+2 step 9,9,15
' V there are 12, 30 degree angles in circle (2*PI) so 2*PI/12 or PI/6
ARC cx,cy,30,0,PI/6,1,14
ARC cx,cy,35,0,RAD(30),1,14
sub legend
at 0,0
"green = leg adj, blue =leg opp, red = hypotenuse = radius"
?"white square is where the right angle is, yellow arcs mark angle in question
?"COS(yellow) = adj/hyp = green/red, red is radius of circle
?"SIN(yellow) = opp/hyp = blue/red, red is radius of circle
?end
Code samples using COS
3d rotating cube with message.bas
3d wire cube v1.bas
3d wire cube.bas
3d_palmx.bas
3d_torus.bas
3dtorus.bas
analog clock.bas
another look at trig functions.bas
autumn scene.bas
B+B.bas
balls in 3d cube.bas
balls in 3d cube.bas
balls.bas
bb2fork smurf.bas
blackjack.bas
BlackJack.bas
blushing snowflakes.bas
boing.bas
bomb.bas
bowling7.bas
bpf1.bas
bpf2.bas
bubbles and triangles.bas
circle trap.bas
clock.bas
clock.bas
crop circles 2.bas
crop circles 3.bas
crop circles.bas
Math
ABS
ABSMAX
ABSMIN
ACOS
ACOSH
ACOT
ACOTH
ACSC
ACSCH
ASEC
ASECH
ASIN
ASINH
ATAN
ATAN2
ATANH
ATN
CEIL
COS
COSH
COT
COTH
CSC
CSCH
DEG
DERIV
DETERM
DIFFEQN
EXP
EXPRSEQ
FIX
FLOOR
FRAC
INT
INTERSECT
INVERSE
LINEQN
LOG
LOG10
M3APPLY
M3IDENT
M3ROTATE
M3SCALE
M3TRANS
MAX
MIN
POLYAREA
POLYCENT
POLYEXT
POW
PTDISTLN
PTDISTSEG
PTSIGN
RAD
RND
ROOT
ROUND
SEC
SECH
SEGCOS
SEGLEN
SEGSIN
SEQ
SGN
SIN
SINH
SQR
STATMEAN
STATMEANDEV
STATMEDIAN
STATSPREADP
STATSPREADS
STATSTD
SUM
SUMSQ
TAN
TANH
TRANSPOSE
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