Tomorrow is my birthday!!!!!! This week I think I messed up big time by not paying attention very well on Tuesday because I was not in the school mood. I struggled a good bit but by Thursday I pretty much had it. I think that the hardest thing is remembering all the formulas and knowing which one goes with what.
Heres the Formulas:
Limacon:r=a+b sin(theta) OR r=a+b cos(theta)
Cardioid:a-b sin(theta) OR r=a-b cos(theta)
Rose:r=a sin(n theta) OR r=a cos (n theta)
n=how many petals
Archimedes spiral:r=a theta+b
Logarithmic spiral:r=a b^theta
Circle with its center at the pole:r=c
Circle that intersects with the pole:r=a sin(theta) OR r=a cos(theta)
The thing I forgot how to do was go from Polar to Rectangular and Rectangular to Polar.
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To convert points from polar to rectangular:
ReplyDeletex=r cos theta y=r sin theta
To convert points from rectangular to polar:
r= +/- sqrt x^2=y^2
theta=tan^-1(y/x)
To convert an equation from polar to rectanular:
-use identities to get rid of any # infront of theta. plug in (y/r) for sin theta and (x/r) for cos theta.
-plug in sqrt x^2+y^2 for r and solve for y.
To convert an equation from rectagular to polar:
-plug in x=r cos theta and y=r sin theta into the equations
-solve for r.