This week we mainly focused on two things and then we learned a little bit on another set of ideals that will be included in the test on tuesday.
the two major things we focused on were memorizing graph shapes and their formulas and converting between rectangular and polar and viseversa
Graph shapes and their formulas
Limacon
r=a+b sin(theta)
r=a+b cos(theta)
Cardioid
a-b sin(theta)
a-b cos(theta)
Rose
r=a sin(n theta)
r=a cos (n theta)
(n=how many petals {if n isodd[#=n] if n is even [#=2n]}
Archimedes Spiral
r=a theta+b
Logarithmic Spiral
r=a^theta b
CONVERTING
when going from polar to rectangular you plug into
X=rcos(theta)
Y=rsin(theta)
and work out until you get a x point and a y point
when going from rectangular to polar you plug into
r=+/- squareroot X^2 +Y^2
and
Theta= (Y/X)
once youve solved for both of these you"ll plug into (+r, theta) (-r, theta)
the only thing i am having trouble with is the converting problems where the answers are already given and you have to solve for the things that were plugged into the equation to get the given answer
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EXAMPLE:
ReplyDeleteGive the polar coordinates for (3,4).
r= +- square root 3^2 + 4^2
r= +- 5
theta= tan^-1(4/3)
theta= 53.130degrees
*which quadrant is (3,4) in? <<<< I
THEREFOR---> the angle in quadrant I goes with the positive 5.
(5,53.130degrees) and (-5,233.130degrees)
Okay well since amy gave you an example of converting to polar, ill give an example of converting to rectangular.
ReplyDeleteConvert (3,30) to rectangular
x= rcos(theta)
x= 3cos30
x= 3(squareroot 3/2)
y= rsin(theta)
y= 3sin30
y= 3(1/2)
your answer is (3 squareroot 3/2, 3/2)
Also dont forget to switch back and forth from degrees to radians depending on the problem!!!