Question

1) Convert the following polar equation of r=2sintheta into a rectangular form.

2) List and find all of the sixth roots of 4.

Answer 1

sel?-0) Given that the polar equation na 2 Sino Convert the polar equation into rectangular form. Noul ours a El e ng sapts yp09 by dif)"w ze EN 2 = 27 Sino) A we know that x=rcoso yarsino Squaring eq uation @ ļo then added them. 22(Sin² of cos?o) x2 + y² = 22 sino + cos?of=1 from equation m2+y? = 244) yersine x2_92-29 zo Ans which is the rectangular form Echtze (А. ea

sol? (2) The sixth roof of 4 are all solution- :326-4=0 (23)?-12-0 (x-2)(x+2) = 0 use thee identity (a b) = (a-b) (afb) (323-6213) (+372)3) Difference of cabes a²_63 = (arb) (a²+ ab +62) 432)3 (1-2)(x+ 2-1/2+ +(32))=0 o 3 x 2-312 =0 & 2°+*.*72 +*2)=0 X = ?[2Ang use the quadratie formula an²tbn+c=0 where as 1, 6-312 Nous, -61 162-400 6=82, C-EFE)? & 26 - 37 1/72 – 4814 ()? 2xl 2 = -17 1 }(313)?(1-4) 2 (:44 x33 =23 13 - 321 322 3 2 26 = -52 317 13.4 Aus ( 77 = +1 +i) 2

And the zeros of +3+372)3 = use the identity sum of cube x²+63 = (a+b) (a² a 6+62) 23+0) = (x+27)(x?- *.17 +°)=0 Hence the zeros of at 72 - 372 and the zeros al 12_x385 +682=0 solve this equation by quadratic equation an2+ batc=0 be -312, CS 2 = we can 2 wher az" (32) NOCO x= -67 V62-44c 2a 2 -F52) I VE720?–48104317) 2x) - + + /637)*(1-4) 2 Jerage 3/2 & (-1)2 = 1 - 3/2 23 2 x = 312 I 32 133 7-3 = 13.11 F) 2 SV3.3 Hence, The all roof is n=1 / 2 1 1 2 3i, an 22 ße Aus 2 2