Q: Starting at the origin, draw a line segment 2 units along the positive x-axis. Draw a second line segment from that point 1 unit in the positive y direction. You are now at point (2, 1), so label this point P. Draw a line between O and P. This line has length r{\displaystyle r} in polar coordinates. It is also the hypotenuse of a right triangle, so you can find the hypotenuse's length using geometry. For example: The legs of this right triangle have values of 2 and 1. With the Pythagorean theorem, calculate that the hypotenuse's length is 22+12=4+1=52.236{\displaystyle {\sqrt {2^{2}+1^{2}}}={\sqrt {4+1}}={\sqrt {5}}pprox 2.236}. The general formula to find r{\displaystyle r} from Cartesian coordinates is r=x2+y2{\displaystyle r={\sqrt {x^{2}+y^{2}}}}, where x{\displaystyle x} is the Cartesian x-coordinate and y{\displaystyle y} the Cartesian y-coordinate. Use trigonometry to find this value: tan()=oppositeadjacent=12{\displaystyle an( heta )={
rac {opposite}{adjacent}}={
rac {1}{2}}}tan1(12)==26.56{\displaystyle an ^{-1}({
rac {1}{2}})= heta =26.56^{\circ }} The general formula to find {\displaystyle heta } is =tan1(yx){\displaystyle heta = an ^{-1}({
rac {y}{x}})}, where y{\displaystyle y} is the Cartesian y-coordinate and x{\displaystyle x} the Cartesian x-coordinate. You now have the values of r{\displaystyle r} and {\displaystyle heta }. The rectangular coordinates (2, 1) convert to approximate polar coordinates of (2.24, 26.6), or exact coordinates of (5,tan1(12)){\displaystyle ({\sqrt {5}}, an ^{-1}({
rac {1}{2}}))}.
A: Consider the point P(2,1){\displaystyle P(2,1)} in the Cartesian plane. Find the distance between the origin O{\displaystyle O} and P{\displaystyle P}. Find the angle between OP{\displaystyle OP} and the positive x-axis. Write down the polar coordinates.

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