Question

for the polar graph of

Answer 1

\[r=\frac{2}{3\sin(\theta)-\cos(\theta)} \] find the restrictions on theta and describe what this will mean in terms of the shape of the graph

Answer 2

since dividing by zero is always a bad idea ....

Answer 3

3sin = cos

3tan = 1

tan = 1/3

Answer 4

\[\tan(\theta)=1/3 \] is not allowed yeah

Answer 5

how will this affect hape of graph ?

Answer 6

i cant be sure, i want to say its asymptotic; but ill have to graph it to be sure

Answer 7

the cartesian form of the equation graphs y=1/3x+2/3 straight line with m=1/3

Answer 8

yes, and that creates a useful alternative, but does not excuse the original defects

Answer 9

so y=1/3x+2/3 would not show the restriction?

Answer 10

it shouldnt.

just like:\(\large \frac{2x^2}{x}\) would translate to the line 2x, but it wouldnt show us the restriction at x=0 since its an algebraic equivalent

Answer 11

when theta hits these angles

http://www.wolframalpha.com/input/?i=3sinx-cosx%3D0

the value of the polar is undefined and therefore cannot be mapped

Answer 12

so just discontinuity at that hpoint

Answer 13

its been awhile, but i do believe that at those intervals we have a jump discontinuity in the cartesian form

Answer 14

and since the limit from left and right are equal, the unbroken straight line is equivalent, but not equal to it

Answer 15

i could very easily be wrong, but i think this does all its business from \(\theta=0\) to \(\theta=2\pi\) it is not a line, but rather a line segment

Answer 16

yeah i am probably wrong

Answer 17

the solution says the line has gradient = 1/3 and so at tan(theta)=1/3, r has infinite solutions? is that correct

Answer 18

the 100 ss would indicate that his wrongest solutions is far better than any correct solutions i may muster ;)

Answer 19

tangent is defined as y/x
gradient is defined as y/x

hmmm

Answer 20

http://www.wolframalpha.com/input/?i=y%3D2%2F%283sinx-cosx%29

if we plot this on a \(\theta r\) plane we can clearly see the asymptotic behavior

each point can be mapped onto the \(xy\) plane, except for the places where the asyptotes exist