Saturday, November 6, 2010

Charlie's.

okay, this week we did chapter 11 and then friday we started on chapter 13, skipping chapter 12.
in chapter 11 we learned the rectangular and polar points.
rectangular=(x,y) & polar=(r, theta)
so what you do is they give you a rectangular point and you change it to polar.
or you are give a polar point and you change it to one or (most likely) two points.
To do this you use the formulas:
r=square root of x^2 + y^2
theta=tan^-1(y/x)
x= rcostheta
y=rsintheta

For example:
(3, 4)
r = square root of 3^2 + 4^2
= square root of 9+16
=square root of 25
=+\-5
r=5
theta= tan^-1(4/3)
=53.13
~now you do a unit circle to see which quadrant it is in~
the tan was positive, so this means that the answers are in
quadrant 1 and 3. so we take 53.13 and add 180.
theta=53.13 & 233.13
so we take the postive theta and put it with the smallest angle.
& we take the negative theta and put it with the larger angle.
Therefore the answer to the problem is...
(5, 53.13) & (-5, 233.13)

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