Sorry for the double post but here is the program. This one explains the math and logic and such. Will get back later with a program that will show it in action. To be honest, this stuff is SO much easier to explain with a white board.
REM: This is a program to demonstrate polar coordinates
LINE 100,300,400,100
Text 0,0,"Here we have a line."
TEXT 0,15,"Basic algebra tells us that every line has a slope, that is, a rise and an run"
TEXT 0,30,"Which will be shown here using red for the rise and blue for the run"
TEXT 0,45,"Press enter to continue"
ink rgb(255,0,0),0
line 400,100,400,300
ink rgb(0,0,255),0
line 100,300,400,300
wait key
ink 0,0
box 0,0,639,60
ink rgb(255,255,255),0
Text 0,0,"Lets call the run the X component and we will call the rise the Y component"
TEXT 0,15,"The distance of this line can represent anything we need, from a speed, to a strength of a force"
TEXT 0,30,"Lets insert the distance of the line (or magnitude for now)"
TEXT 0,45,"Press enter to continue"
wait key
distance#=sqrt(300^2+200^2)
Text 200,175,str$(distance#)
wait key
ink 0,0
box 0,0,639,60
ink rgb(255,255,255),0
Text 0,0,"Now we will calculate the angle using basic trig."
TEXT 0,15,"First though, lets review SOHCAHTOA"
TEXT 0,45,"Press enter to continue"
wait key
cls
PRINT "SOH means: Sine=Opposite/Hypotenuse"
PRINT "Where Opposite is the length of the side of the triangle opposite of the angle itself"
PRINT "and Hypotenuse is the length of the longest side (for our purposes, it is the magnitude)"
PRINT " "
PRINT "CAH means: Cosine=Adjacent/Hypotenuse"
PRINT "Where adjacent would be (obviously) the length of the side of the triangle next to the angle"
PRINT "note that this is NOT the hypotenuse"
PRINT " "
PRINT "TOA means: Tangent=Opposite/Adjacent"
PRINT "So what does this mean with the triangle for the triangle?"
wait key
cls
LINE 100,300,400,100
Text 200,175,str$(distance#)
ink rgb(255,0,0),0
line 400,100,400,300
text 405,200,"200"
ink rgb(0,0,255),0
line 100,300,400,300
text 300,305,"300"
ink rgb(255,255,255),0
Text 0,0,"So, tangent=red/blue"
Text 0,15,"Therefore, tan(angle)=200/300=2/3"
TEXT 0,30,"Taking the arctangent, we find that atan(2/3)=angle"
TEXT 0,45,"Think of the arc trig fucntions (arcsin, arccos, and arctan)"
TEXT 0,60,"will return the angle whose function is what is passed to it. In this case, angle whose tangent is 2/3"
wait key
ink 0,0
box 0,0,639,75
ink rgb(255,255,255),0
angle#=atan(.66)
Text 0,0,"atan(.66)="+str$(angle#)
TEXT 0,15,"Now lets change things. Now we will know the magnitude and the angle, "
TEXT 0,30,"but we won't know the components"
text 123,283,") "+str$(int(angle#))
wait key
cls
LINE 100,300,400,100
Text 200,175,str$(distance#)
ink rgb(255,0,0),0
line 400,100,400,300
ink rgb(0,0,255),0
line 100,300,400,300
ink rgb(255,255,255),0
text 123,283,") "+str$(int(angle#))
text 0,0,"Once again, we go back to SOH CAH TOA"
text 0,15,"Which shows us that Sine=Opposite/Hypotenuse and Cosine=Adjacent/Hypotenuse"
Text 0,30,"By multiplying the function (sine or cosine) by the hypotenuse, we can find the side lengths."
wait key
ink 0,0
box 0,0,639,75
ink rgb(255,255,255),0
TEXT 0,0,"First to find Red. We take sine of 33, which is "+str$(sin(33))+"."
TEXT 0,15,"Then, since Sine=Opposite/Hypotenuse, we can multiply to get "
TEXT 0,30,"Sine*Hypotenuse=Opposite"
TEXT 0,45,"So, Sin(33)*"+str$(distance#)+"=Opposite, or the Y component (the rise)"
TEXT 0,60,"This gives us a value of " +str$(sin(angle#)*distance#)+ " which is what we knew before to be true (plus or minus due "
TEXT 0,75,"to rounding problems)"
wait key
ink rgb(255,0,0),0
text 405,200,"200"
ink 0,0
box 0,0,639,90
ink rgb(255,255,255),0
TEXT 0,0,"So now we know the hypotenuse and the opposite side length"
TEXT 0,15,"To find the adjacent side, we can do a couple of things"
TEXT 0,30,"1. We can use divide the Y component (opposite) by the tangent to get it"
TEXT 0,45,"2. We can use pythagorean's theorem (a^2+b^2=c^2)"
TEXT 0,60,"3. We can multiply cosine by the hypotenuse to find the X component (adjacent)"
wait key
ink 0,0
box 0,0,639,90
ink rgb(255,255,255),0
TEXT 0,0,"Even though the others may seem easier, we will go with number 3"
TEXT 0,15,"because it doesn't need the y component (and thus, we would only"
TEXT 0,30,"need to perform 1 calculation in total, rather than 2"
wait key
ink 0,0
box 0,0,639,90
ink rgb(255,255,255),0
TEXT 0,0,"So: Cos=Adjacent/Hypotenuse and therefore Cos*Hyp=Adj"
TEXT 0,15,"The math: Cos(33)*"+str$(distance#)+"=Adj="+str$(cos(angle#)*distance#)
TEXT 0,30,"Which confirms what we already knew from before, that is, that the X component is 300"
wait key
text 300,305,"300"
[EDIT]
BTW guys, what ideas do we have for the next project?
My suggestion is that we go with a Zelda style adventure game (perhaps, depending on how we do, next time we can move into a simple rpg or something). What other suggestions do you guys have?
Great Quote:
"Time...LINE??? Time isn't made out of lines...it is made out of circles. That is why clocks are round!" -Caboose
