Question

[7] Rectangular coordinates of a point are given. Find the polar coordinates for each point such that r20 and 050<21. Sketches have been provided on the scratchwork page. (-2,-2/3) (8, - 8) (-2, 0) (-24, 7)

Answer 1

(x, y) =(-2,-2113) Point lies in trd quadrant. ..o= tant (he) +84 180° = tant (-283 ) + 180° tant (13) +180° 60°t 180 = 240° And r= Joe?ty² = J (-23²+ (-2153)² ieor=5 4+12= =J16 = 4 - le r=4 Hence, polar co-ordinates are. (x,y) = ( 4 os 240°, 4 sin 2400) le. (2 M) = (8,8) point lies in th quadrant. tan' (1) = tant (-3) = tant (-1) = $15° = 315) And se²ty²= 58²+(-8,² =564+64 64+ 6 4 = 852. Hence, polar co-ordinates (x,y) = Croosd, roina) = C 812 US 315 8 12 sin 315) ar

3. C-5o) ter point is on & -ve x-axis. o = tant ce e ) + 180° = tant Cos) +180° 0° +180° 180° And r=√xe²+ y² = J (-2)²+02 JU polar co-ordinates ar. (RM)=Creosorsino) =( r ws 1800 ot sin 1800) C -24,7) Here point is in and quadrant = tant (2 e) + 180° e tant ( 23 24 ) +180° - 16.26° +180° = 163.740 And Jx²44² = √ (-243²+ 7 = √576+49 :. polar co-ordinates are. = re (2,4) = (25 cos 163.74, 25 sin 163.740)