Question

polar form. Can someone clarify my teachers notes.. ?

Answer 1

post

Answer 2

(blue box) Why did we need to add pi ?

Answer 3

when both the co-ordinates are negative,
in which quadrant does the point lie ?

Answer 4

3rd!

Answer 5

but why add the pi? ):

Answer 6

think where (-5, -2) lies in xy plane

Answer 7

yes,
and since tan is periodic with \(\pi\)
we can add or subtract pi, to change the quadrants, without changing the tan value!

Answer 8

hm, for some reason i can't comprehend that :|

Answer 9

what is tan^-1 of 1
?

Answer 10

pi/4

Answer 11

okay, lets not add pi and see what we get in polar

Answer 12

what if i say, the point i am looking for is in 3rd quadrant, but has the tan inverse as 1 only ?

Answer 13

(-5, -2) = (sqrt(29), 0.381) ?

change the angle into degrees and see where you land

Answer 14

@hartnn well i agree thats where you would have to add something to move elsewhere?

Answer 15

yes, i need the move the point from quadrant 1 to Quadrant 3, but tan value should remain same,
so i use the fact that since tan is periodic in pi
(after pi radians, tan values repeat)
i just add pi to bring the point in 3rd quadrant

Answer 16

hmm i understand. I guess i had trouble with this because i wasnt sure when i would know that i would need to add pi @hartnn

Answer 17

i would just need to know the trend of tangent huh?

Answer 18

yes,
periodicity of each ratio, not only tan

Answer 19

eek ok. maybe i can look on youtube for similar examples!

Answer 20

\((r, \theta) = (-r, \theta + \pi)\)

\(r = \pm \sqrt{x^2+y^2}\)

Answer 21

And, keep in mind there is no single way to represent a point in polar unlike the unique representation in cartesian

Answer 22

the mistake in your work is that u have ignored \(r = -\sqrt{29}\)

Answer 23

the reason your teacher added pi is because arctangent only gives you an angle between -pi/2 and pi/2 (1st or 4th quadrant)

so when you do arctan(-2/-5), even though the x,y coordinate are in the third quadrant, it still gives you an angle, in this case, in the first quadrant.

So the get to the third quadrant, add pi to arctan(2/5) because tangent has period of pi

Answer 24

@sourwing great explanation! definitely helped much more

Answer 25

thank you @sourwing!