Question

this is the second time i post this please do it right this time and show all the steps

(10 pts) 3. Find the area inside the asteroid given by the parametric equations x=4cos') and y4sin' for OSIS2.. Show the setup of the integral and use your TI84's "fnint command to find the area.. (10 pts.] 4. Find the arc length of the asteroid given by the parametric equations x=4cos' (/) and y4sin) for Osis 2. Show the setup of the integral and show all steps to integrate and evaluate manually to find the arclength. [10pts.] 5. Find dy and the equation of the tangent line at the point (x,y) (-2, 0) on dx the curve r -211-sin()). Include a graph of the polar curve with the orienation indicated

Answer 1

a) 6π . b) 24 . c) y=x+2

fron) (40) x= 4 cog3 (4) Y=:4 sin3 (+) ostean We first find the area of the (4,0) crive in the est quadrant. 160-4) If y = f(x) Then the area in Cheonda dx=-120077sin tad 719) f(400531+ 294) nell 4 rin3 (+) In the 1st quadrant osts the ². Area in 4 0 T2 • 7/2 So" 48 sin(t) cos² (t) et 2 sine (t) et So 1204 sin (H) cos() Som2 6. (5m2=5". ("+c924) dt *S" 3:(1-094 )(1-1924) de 1- (024 - Con H+ đeoá Đova (1 ) - *12 3 So

TI z 23 S. C0947- Comet + (600 67 t co2 2+) dt 2 I The cogatct t 3 3 cost et + 3 con ltd conut o 7" T42 (Smar m =3 3 Sinat 2 1/2 +3 (smót 6 2 t 3 (12) -3 [ sinut 2 o 2 h 0 31-0-0 -o toto 371 2 The 6TL area in the 1st quadrant in 37/2 : Total area bounched by the curve is 4x 37 5) The are longle of a fewea metie Jumelion is given by B L 1-(1997 (99 de OS5 272 3t 2 = 4 con y = 45 in3 f da 12con sint dy - 12sint cost at et :: Anc length of the asteroid in the lef quadrant ing 1/2 2= 11/2 It (coort) + sin(t)) 71/2. sinatet T1/2 . 65. J. (120ortsint) & (12 in Frost)? at sa desno+5 t) 12% to Cont sint -6124 8 [-12/ are length of the asteroid ob 6x4=24 = -6 - 6 is Total

3). r=2(1-rina) rai-2c000 Given point db (2,4)= (-2,0) n = r cona y=rsino a' r'eosorsino is o=rsino => a=11, r=2 =rcoso telsina dy dy/dla risina t r cosa an - rsino Y' dalda r'cono N -2 cogasina + 2cona -25'na cosa - 2coo o cosa asmo +2sma con Sinza - cosa Sino t conzo i dy dy da z 1 an DTL (-2,0) Equation of tangent is (1-0) = (2+2) >> Ya+2 • (-2) (977) (20) - 12,0)

r=2(1 – sin ) <O< 21 0 2 Nx+2 x r=1 -10 10 x 7= 2 -10 -8 -6 6 -10 10 Х 1 = 3 -10 10 Х 7=4 -10 10 Х y = -tan SIS