Question

Determine two pairs of polar coordinates for the point (4, 4) with 0° ≤ θ < 360°

Answer 1

use
x=rcos(theta)
and
y=rsin(theta)
from here u can determine theta
can u do it?

Answer 2

not quite, what is r again?

Answer 3

look in cartesian coordinate system there are mainly two coordinates which is (x,y) and
in polar system the coordinates are expressed as (r,theta)
caresian x is expressed as
\[x=rcos(\theta)\]
and cartesian y is expressed as
\[y=rsin(\theta)\]
make sense?

Answer 4

yes

Answer 5

so
\[\frac{ x }{ y }=rcos \theta/r \sin \theta\]
so \[\tan \theta=y/x\]and
then\[\theta=\tan^{-1} (\frac{ y }{ x })\]
ok so far?

Answer 6

yes

Answer 7

so now just put x=4 and y=4
so whats the value of theta?

Answer 8

pi/4

Answer 9

good
so theta is evaluated now we need to calculate r

Answer 10

for r --
find \[x^2+y^2\]
can u do it?

Answer 11

32

Answer 12

yes
so it would be equal to r^2 now
ok with this?

Answer 13

yes

Answer 14

\[x^2+y^2=r^2(\cos^2 \theta+\sin ^2 \theta)=r^2\]
\[r=\sqrt{x^2+y^2}=\sqrt{32}=4\sqrt{2}\]
got this?

Answer 15

yes

Answer 16

so the polar coordinates are
\[(4\sqrt{2},\frac{ \pi }{ 4 })\]

Answer 17

ok

Answer 18

good :)

Answer 19

But the answers are in degrees, so do we need to convert?

Answer 20

yeah u can write (pi/4) equal to 45 degree

Answer 21

ok, thanks

Answer 22

yw!

Answer 23

and u can click "best response" button if u feel that my help is enough ^_^