Question

How do you convert `(4, 2pi/3)` to rectangular form?

Answer 1

`((-2),(2sqrt3))`

Explanation:

To convert from `color(blue)"polar to cartesian form"`

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(x=rcostheta , y=rsintheta)color(white)(a/a)|)))`

here r = 4 and `theta=(2pi)/3`
`color(blue)"--------------------------------"`
`x=4cos((2pi)/3)`

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(cos((2pi)/3)=-cos(pi-(2pi)/3)=-cos(pi/3))color(white)(a/a)|)))`

`rArrx=-4cos(pi/3)=-4xx1/2=-2`
`color(blue)"------------------------------------------------------------"`
and `y=4sin((2pi)/3)`

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(sin((2pi)/3)=sin(pi-(2pi)/3)=sin(pi/3))color(white)(a/a)|)))`

`rArry=4sin(pi/3)=4xxsqrt3/2=2sqrt3`
`color(blue)"---------------------------------------------"`

Thus the components of the vector `=((-2),(2sqrt3))`