Question

[16] In what quadrant of the polar plane does the polar point (-15, - 91°) lie? A. B. 1 c. III D. IV E. it lies on an axis [17] In what quadrant of the polar plane does the polar point (12,3) lie? A. B. 11 c. D. TV E. it lies on an axis [18] Determine the product: ( cis )( cis ) A. m, cis 0,0. B. (+ 5) cis 0,0; C. 11cis (, + ) D. (5 + ) cis (@, + ®,) [19] Determine the quotient: Pcise Kcis L A. P K cis į B. (P - K) cis C. (K – P) cis , D. cis (Q - Z) E. cis (L - Q) [20] Simplify (R cis )'. A. Rp cis pe B. Rcis pe C. Rp cis 6 D. Rcis P E. none of these [21] Which polar point is not equivalent to the polar point (20,- 700º)? A. (20, 20°) B. (-20, 200) c. (-20, -160) D. (20,- 340) E. not one of these is not equivalent, meaning they are all equivalent [22] Which polar point is not equivalent to the polar point (-34, – 37)? A. (34,0) B. (3x, 37) C. (-37,-) D. (-37, ) E. not one of these is not equivalent, meaning they are all equivalent [23] Which polar point is not equivalent to the polar point (-6, 12 7 A. (6,- 197 12 B. 6, c. 197 12 D. 6. 17 12 E. not one of these is not equivalent, meaning they are all equivalent

Answer 1

16 Given (-15,- 910) 2= 800S0 = -15 (OS (-91°) = 0.26 yoysimo = -15 sim (-910) = 14.99 So, it lies in 1st Quadrant (option A) 11 (12,3) (12,3) Quadrant 18 Product of (,ciso, ) (72. Cis 02) 9, (cose, tú sine,) 9 (6050, +usim 82) > 0, Oz (cose, tusimo, ) (cos®2 + u sim (2) 3) 8,82 (COSO, cos®, + u simo, cose, tucoso, simez + i 2 simo, sim oz) ) 0,02 (c058, cose, - sine, sime, + u(sim 6, cosez + cose, sinez)) 300 cos (0,402) + u sim ( 0, +82)} 8,82 cis (01+0₂) (option ) Pcis a P (cosa tusime) (cOS L-usimL) k ( cosL + u simL) (605L-usim) 19 Х Kcis L P K COS& COSL tusima.cos L-usimL COS Q-ja sinasimL (OSL) ² - ( isimL) ² Cos (0-L) tu sim (Q-L} K i sim (8-2)] 1 cis (Q-L) option D K

Р 20 (R cis e)!= {R (c030 + usime cos po + usim pe) RP (cos option (B) 21 Polar Point (20,-700) 22 - YCOSO - 20 cos (-700°) - 18-194 y = r simo 20 sin (-700*) - 6-8404 According to x.y from we com check which is not equivalent ay (20,209) = x = 2000S 20° = 18-194 equivalent 8 - 20 sim 20 - 634 b) (-20, 200°) : X-2000S 200º = 18.794 Equivalent y = -20 sim 200° = 6-84 C) (-90,-160) x= -20 COS(160°) - 18.794 y = -20 Sim (-160°) = 6184 Equivalent d) (20,-340") = X 20 COS(-340) = 18.794 Equivalent ya - 20 sim (-340) - 6184 option (E) is correct 22 (-37, -3x) X=-37COS (-3X180°) = 36 Y = -34 sim (-3x180°) = 0 a> (31,0) - x= 31 (OSO = 3A Y = 3 À Simo=0 equivalent b) (34, 31) - 06:37 COS 31 a -ZA Not equivalent Y = 3a sim 3a = 0

23 Polan Point (-6,99) 57 12 -- 10553 X= 8 coso = -6 cos Y = rsimo = -6 sosim SX = -5.795 12 Now , 5x 12 X 180 = 75° it is equi valent to 75 4 180° = 255° because point lie in 3rd Quadrant So, if >0,0 = 255° 255 X_R 180 177 12 8 so. (6.172) it equivalent to (-6,52) And Also check ay (-6,5192) by 16, -73) OL= -6 605 (192) = -|-55 y = -6 sim ( 192 ) = -5.795 x= 6 cos (72) = -1:55 y = 6 sin (75) = -5.799 x = 6 cos (1952) = 1:55 y = 6 sim c) (6,-192) - Not equivalent (192) = 5.795 Coption e).