Convert 3 pi into rectangular coordinates Convert 5 3 pi2 in

Convert (3, pi) into rectangular coordinates. Convert (5, 3 pi/2) into rectangular coordinates. Convert (8, pi/3) into rectangular coordinates. (4, 4 squareroot 3) (8, squareroot 3/2) (4 squareroot 3, 4)

Solution

question1

convert(3 ) into rectangular co-ordinates.

let(x,y)=(3,) A=xcosy

                          =3cos     {cos=-1}

                          =3(-1)=-3     so A=-3

           B=xsiny

            =3sin         {sin=0}

            =3(0)=0     so B=0

The rectangular co-ordinates of (3 ) is (A B) = (-3 0).

question2

to convert(5 3/2)into rectangular co-ordinates.

let (x y)=(5 3/2)

A=xcosy

=5cos3/2    

=5(0)                (cos3/2=0)

=0

B=xsiny

=5sin3/2

=5(-1)          (sin3/2=-1)

   =-5

so the rectangular co-ordinates of (5 3/2) is (A B)=(0 -5)

question3

to convert (8 ÷ 3) into rectangular co-ordinates.

let (x y)=(8 ÷ 3)

    A=xcosy=8cos ÷ 3

                =8(1/2)                   { cos ÷ 3 value is 1/2}

               =4

   B=xsiny=8sin ÷ 3

               =8(3/2)

                =43

so The rectangular co-ordinates of (8 /3) is (A B)=(4 43)