anonymous
  • anonymous
write each polar equation in rectangular form: r=-3sec(Theta) r=costheta+sintheta r=5/3costheta+8sin
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
^theta after the last sin
myininaya
  • myininaya
You need to use these equations: \[r^2=x^2+y^2 ; rcos(\theta)=x ; rsin(\theta)=y \]
anonymous
  • anonymous
i did, but like it ended up like x^2+y^2= 25+9x^2r^2-30xr/64y^2 for the last one

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myininaya
  • myininaya
We want the equations just in terms of x and y instead of r and theta.
anonymous
  • anonymous
i don't know what i did wrong
myininaya
  • myininaya
so the last one is: \[r=\frac{5}{3}\cos(\theta)+8\sin(\theta) \]?
anonymous
  • anonymous
no uh (5)/(3costheta+8sintheta)
myininaya
  • myininaya
oh so you meant 5/(3costheta)+8sin(theta)) and not 5/3cos(theta)+8sin(theta)
anonymous
  • anonymous
mhm 5 / (3cos+8sin)
myininaya
  • myininaya
\[r= \frac{5}{3\cos(\theta)+8\sin(\theta)}\] Multiply both sides by that one fraction's denominator
myininaya
  • myininaya
\[r(3\cos(\theta)+8\sin(\theta))=5 \] Distribute then substitute the equations I gave you
anonymous
  • anonymous
3xr+8ry=5 but then you'll need to put r on one side cause you would need to square it. and the answer comes out all weird
myininaya
  • myininaya
well rcos(theta) is x not just cos(theta same thing with the y deal rsin(theta) is y not just sin(theta)
anonymous
  • anonymous
whoops how about the secant one
myininaya
  • myininaya
put it in terms of cos by using an identity
myininaya
  • myininaya
then put it in some form where you can use the equations I gave you
anonymous
  • anonymous
sosoososososo it would be x^3+y^2x=-3 AND uh the other one x^2+y^2=x+y?
myininaya
  • myininaya
for the first one? no...
myininaya
  • myininaya
I haven't looked at the second one... You are making this way too hard it looks like.
myininaya
  • myininaya
first one you did this as first step right?: \[r=\frac{-3}{\cos(\theta)}\]
anonymous
  • anonymous
yep
myininaya
  • myininaya
Notice this only has a cos in it... how do you get cos with the r over there so you can use the equation rcos(theta)=x
anonymous
  • anonymous
multiply both sides with r
myininaya
  • myininaya
no
myininaya
  • myininaya
try again
myininaya
  • myininaya
How do you undo multiplication?
myininaya
  • myininaya
Or division?
anonymous
  • anonymous
oh omg
myininaya
  • myininaya
we have division by cos to undo that you ?
anonymous
  • anonymous
x=-3
myininaya
  • myininaya
yes
anonymous
  • anonymous
thanks
myininaya
  • myininaya
so for that second one...
myininaya
  • myininaya
you actually got it right
myininaya
  • myininaya
but how did you go about it you didn't choose a complicated way right?
anonymous
  • anonymous
yep uh multiplied both side with r and then substituted the stuff in
myininaya
  • myininaya
oh good
myininaya
  • myininaya
do you have any other questions? do you think you got this better?
anonymous
  • anonymous
uh yea i have a few more
anonymous
  • anonymous
for standard forms of polar equation uh how would graph r=2cos3theta
myininaya
  • myininaya
Plug in values of theta and see what the r output is
myininaya
  • myininaya
then remember how you graph using polar coordinates r is the distance from the origin and direction is given by r to from the angle theta is the angle
anonymous
  • anonymous
like how would you do this with a graphing calculator
myininaya
  • myininaya
So for example if I plug in theta=0 \[r=2 \cos (3 \cdot 0)=2\cos(0)=2(1)=2 => \text{ graph the point } (2,0^o)\] |dw:1388269865874:dw|
myininaya
  • myininaya
find 0 degrees and then go to the circle with radius 2
anonymous
  • anonymous
cause wksht says not to use a table
myininaya
  • myininaya
|dw:1388269927627:dw| then plug in more points
anonymous
  • anonymous
oh i know how to graph but not without plugging in points
myininaya
  • myininaya
I haven't looked at a calculator in ages
myininaya
  • myininaya
did you try looking up how to input polar equations into whatever calculator type you have
myininaya
  • myininaya
some calculators require a difference procedure in order to do certain things
myininaya
  • myininaya
http://mathbits.com/MathBits/TISection/PreCalculus/polargraphs.htm
myininaya
  • myininaya
find mode and choose polar or pol or polargc
myininaya
  • myininaya
then just type your equation in
anonymous
  • anonymous
u what's the website
anonymous
  • anonymous
*uh
myininaya
  • myininaya
What ?

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