09.02 - 9.2 GRAPHENG IN POLAR COORDINATES l. 3. 1 +...

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Unformatted text preview: 9.2 GRAPHENG IN POLAR COORDINATES l. 3. 1 + cos(—6) : 1 + cos 6 = r :> symmetric about the x-axis; 1 + cos (—0) # —r and 1 + cos (7r — 9) m 1 — cos 0 ¢ r :1» not symmetric about the y-axis; therefore not symmetric about the origin 1—sin(—6)= 1+sin07£rand1—sin(1r—0) = l — sin 9 75 —r => not symmetric about the x-axis; 1— sin(1r —0) m 1 — sin 0 m r 2> symmetric about the y-axis; therefore not symmetric about the origin 2+sin(—9)=2—sin07£rand2+sin(1r—t9) = 2 + sin 0 5£ —r => not symmetric about the x-axis; 2 + sin(1r — 6) = 2 + sin 0 = r => symmetric about the y-axis; therefore not symmetric about the origin sin (— g) = — sin (3;) = —r => symmetric about the y-axis; sin = sin , so the graph i_s symmetric about the x-axis, and hence the origin. cos(—0) : cos 0 = r2 :> (r, —0) and (—r, —0) are on the graph when (r, 0) is on the graph => symmetric about the x-axis and the y-axis; therefore symmetric about the origin 11. 13. 15. 17. 19. —-sin(7r——0) = —sinél=r2 => (r,7r ~0)and(—r,1r—0) are on the graph when (r, 6) is on the graph => symmetric about the y-axis and the x-axis; therefore symmetric about the origin Since ( :i: r, —0) are on the graph when (r, 0) is on the graph (( :1: r)2 = 4 cos 2(— 0) => 1'2 = 4 cos 20) , the graph is symmetric about the x-axis and the y-axis => the graph is symmetric about the origin Since (r, 0) on the graph :> (—r, 0) is on the graph ((:l:1’)2 = —sin20 => r2 =—sin20) ,thegraphis symmetric about the origin. But — sin 2(—0) : —(— sin 20) sin 20 yé r2 and — sin 2(1r — 6) = — sin (27r — 26') 2 — sin (—20) m —(— sin 20) 2 sin 20 ¢ 1'2 2> the graph is not symmetric about the x-axis; therefore the graph is not symmetric about the y-axis 6:g:>_r=—1=>(—1',%),and0=-%=> r=—1 r’ sin 0+r cos 3 r’ cos 9—: sin 9 :>(_1’_%);fm gig~—_~—sin6;Slopem __ wsin29+rces a m sinBcos 0~r sinB — sin2 (1) +(—-1) cos 1 _W_L’r—%r : at (—19— is —sm -2- cos -2-—-(—l) Sin i => Slope at (—1, is 6 {2349:200526; __ I’Sinfi-Hcosfi __ 2c0823sin9+reost9 _ r’cos 9—1' sint9 _ 2605 29 cos 0—! sint9 Zooslil sin(%1+(1)cos(%l .. T, . : Slopeat (1’: ,, , 2cos(—-E)sinl-El+(*i)c°sl“£l _ . Slope at (-L- :{l 18 _ 1’ 2cos(3—2—") sin(3;—’F)+(-UCOS Zeus 175 3" —(—1)5ii1 3;? 2 005 T 2cm (" Sin (" %)+(l)cos (— 34—7" Slo at 1—31 is 2 pa (5 4) Quasi—3275icosi—éf-i—(inmi—all Slope Slope at (—1, 37"" is = 1; —1 (b) 23. (a) (b) 25. 27. 05r£2~2ms0 31. 32. ...
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09.02 - 9.2 GRAPHENG IN POLAR COORDINATES l. 3. 1 +...

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