Polar Coordinates Introduction (I) - Ch.10

II. Polar Coordinates INTRODUCTION (Ch.10) I POLAR COORDINATES the Polar Plane: series of concentric circles focused about the pole a polar coordinate (ro) is a given radius and angle in standard position angles are in radians Iradius unit (r.) radius angle (rad) II. GRAPHING i. locate ii. count radii from the pole ↳ if \(r<0,\) count in the opposite direction 1. plot (2,꽃) 2. plot (4,-플) 3. plot (-2,3) III CONVERT RECTANGULAR-TO-POLAR: when converting rectangular-to-polar, the following facts will be used: tanor² \(r^{2}=x^{2}+y^{2}\) 4. convert (2,1) to polar coordinates (2) \(tan~\theta=\frac{1}{2}\) \[\theta=\frac{3\pi}{20}\] \(r^{2}=\underline{(2)}^{2}+(1)}^{2} (\sqrt{5},\frac{3\pi}{20})\) \[r=\sqrt{5}\] 0 \[\theta=tan^{-1}(\frac{1}{z})\] convert (4,-5) to polar coordinates 6. convert (8,2) to polar coordinates \[tan~\theta=\frac{-5}{4}\] \[tan~\theta=\frac{1}{4}\] (5-2) \(\theta=tan^{-1}(-\frac{1}{4})\) \[\theta=\frac{173\pi}{90}\] \[\theta=tan^{-1}(-\frac{5}{4})\] \[\theta=\frac{103\pi}{60}\] θ r \[r^{2}=(q)^{2}+(-2)^{2}\] \[r=2\sqrt{17}\] r \[r^{2}=(4)^{2}+(-5)^{2}\] \[r=\sqrt{41}\] \[(x-5)\] \[(2\sqrt{17},\frac{173\pi}{90})\] \[(\sqrt{41}_{s}\frac{103\pi}{60})\] IV. CONVERT POLAR-TO-RECTANGULAR when converting polar-to-rectangular, the following facts will be used: γ- γιοςθ \[y=r~sin~\theta\] 7. convert \((4,\frac{\pi}{3})\) to rectangular coordinates \[x=4~cos\frac{\pi}{3}\] \[x=2\] \[(2,2\sqrt{3})\] \[y=4~sin^{\frac{\pi}{3}}\] \[y=2\sqrt{3}\] 8. convert \((-5,\frac{\pi}{3})\) to rectangular coordinates \[x=-5~cos\frac{\pi}{3}\] \[x=-2.5\] (-2.5,-4.3) \[y=-5~sin\frac{\pi}{3}}\] \[y=4.3\]