Question

Convert 3 – 3i to polar form.

Answer 1

take ,
r cos theta = 3
r sin theta = -3

now,
r^2 (cos^2 theta + sin^2 theta) = ?

Answer 2

i got 0? @gemini208012

Answer 3

How did you do it ?

Answer 4

oh wait 18? I because don't just square the two and add them?

Answer 5

@gemini208012

Answer 6

yes so,
if r^2 = 18
then, r = root 18

Answer 7

so my answer would be 18?? @gemini208012

Answer 8

now put the value of "r" in the first two equations.
which is
r cos theta = 3
cos theta = ?
and
r sin theta = -3
sin theta = ?

Answer 9

I'm sorry I'm confused pre-cal is not my subject! @gemini208012

Answer 10

cos theta = 3/r
cos theta = 3/root 18
and
sin theta = -3/r
sin theta = -3/root 18
did you get it ?

Answer 11

eh no I picked 0 I didn't know @gemini208012

Answer 12

what is it that you did not understand ?

Answer 13

the whole set up period like I didn't know where to plug in the numbers @gemini208012

Answer 14

see earlier we had
r cos theta = 3
we calculated r^2 = 18
so r = root 18 (by removing square from "r")
now to the first equation we had

r cos theta = 3
root 18 cos theta = 3 (putting the value of "r")
cos theta = 3/root 18
and similarly for sin theta .

Answer 15

which will be
\[\sin \theta = -3/\sqrt{18}\]

Answer 16

so we have
\[\sin \Theta = -3/\sqrt{18}\]
\[\cos \Theta = 3/\sqrt{18}\]

Answer 17

And those cancel out right? @gemini208012

Answer 18

Yes
cancelling will give you
\[\sin \theta = -1/\sqrt{2}\]
\[\cos \theta = 1/\sqrt{2}\]

Answer 19

but then those wouldn't cancel either? @gemini208012 that's where I keep getting stuck .

Answer 20

See you can write
\[\sqrt{18} = \sqrt{3 * 3 * 2}\]

Answer 21

which is
\[\sqrt{18} = 3\sqrt{2}\]

Answer 22

that would be the final answer ? @gemini208012

Answer 23

no . Now that you have the values . You need to write them in the pi form.

Answer 24

3pi/4? @gemini208012

Answer 25

No. See that the sin theta is "minus".

Answer 26

sin theta is minus in the third quadrant.

Answer 27

fourth quadrant will also do it.

Answer 28

lol i'm just confused! @gemini208012

Answer 29

You can write 7pi/4, but 5pi/4 will also do it. because cos -theta = cos theta

Answer 30

Now you know the value of r and both sin and cos.
Write them in the form of
r(cos theta + i sin theta)

Answer 31

I give up lol @gemini208012

Answer 32

it will be
\[\sqrt{18} (\cos 7\Pi/4 + i \sin 7\Pi/4)\]

Answer 33

Did you get it ?

Answer 34

Okkkkkkay I kinda see what your saying now @gemini208012

Answer 35

lol it is not that hard. Just practice. I was also confused like you the first time I solved them.

Answer 36

You helped me out though thank you so much! @gemini208012

Answer 37

You are welcome. @Tashaydavis63