Question

What are the components of the vector between the origin and the polar coordinate `(9, (4pi)/3)`?

Answer 1

`((-9/2),(-9/2sqrt3))`

Explanation:

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

`"that is "(r,theta)to(x,y)" using"`

`•color(white)(x)x=rcosthetacolor(white)(x);y=rsintheta"`

`"here "r=9" and "theta=(4pi)/3`

`•color(white)(x)cos((4pi)/3)=-cos(pi/3)color(white)(x);sin((4pi)/3)=-sin(pi/3)`

`rArrx=9cos((4pi)/3)=-9cos(pi/3)=-9xx1/2=-9/2`

`y=9sin((4pi)/3)=-9sin(pi/3)=-9xxsqrt3/2=-9/2sqrt3`

`rArr(9,(4pi)/3)to(-9/2,-9/2sqrt3)to((-9/2),(-9/2sqrt3))`