Question

How do you convert `(4, pi/6)` to rectangular form?

Answer 1

`(4,pi/6)to(2sqrt3,2)`

Explanation:

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

That is `(r,theta)to(x,y)`

`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=pi/6`

`color(orange)"Reminder"`

`color(red)(|bar(ul(color(white)(a/a)color(black)(cos(pi/6)=sqrt3/2" and " sin(pi/6)=1/2)color(white)(a/a)|)))`

`rArrx=4cos(pi/6)=4xxsqrt3/2=2sqrt3` and

`y=4sin(pi/6)=4xx1/2=2`

Thus `(4,pi/6)to(2sqrt3,2)`