Question

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Answer 1

To convert from one to the other, you need to solve the triangle:

Polar Coordinates you mark a point by how far away, and what angle it is:

Answer 2

so first you solve for r using Pythagorean theorem and then solve tan opp/adj
and oyu will get your polar coordinates (hypotenuse,degrees)

Answer 3

so -1,0 gives 1, 2pi?

Answer 4

no

Answer 5

\[r=\sqrt{(-1)^{2}+(\sqrt{3})^{2}}\]

Answer 6

and tan theta = opp/adj

Answer 7

you can also solve by this method.
\[put -1=rcos \theta,0=r \sin \theta \]
square and add,
\[r ^{2}\left( \cos ^{2}\theta+\sin ^{2}\theta \right)=\left( -1 \right)^{2}+\left( 0 \right)^{2}=1,r=1\]
\[-1=1\cos \theta ,\cos \theta=-1=\cos \pi,\theta=\pi \]
\[\left( -1,0 \right)=\left( 1\cos \pi,1\sin \pi \right)\]

Answer 8

\[\left( -1,0 \right) \in polar coordinates is \left( 1,\pi \right)\]

Answer 9

\[it is not (1,2 \pi) \]