Question

A(11,-70`) B(8,80`) polar coordinates
Find the two possible polar angles for the line segment of the above which specify the inclination of the line.

Answer 1

here we are ..
we want to find just piece of line inclination of AB and it must be in polar also.



so we have to shift AB line and make point A to the origin so it be like that .. i refer it to A' and B' cause its different from original




This is the Idea .. Lets begin to implement it

A(8,80') polar = (1.389,7.878) Cartesian
B(11,70') polar = (3.762,-10) Cartesian

B-A = (3.762-1.389,-10-7.878)=(2.373,17.878)

\[r=\sqrt{2.373^{2}+17.878^{2}}=18.035\]
\[\theta 1=270+\tan ^{-1} \frac{y}{x}=270+82.4=352.4 \]
\[\theta 2= -90+82.4=-7.6\]

(18.035,352.4') polar and (13.035,-7.6) polar

Hope I'm right .. regards