What are the components of the vector between the origin and the polar coordinate $(4, (11pi)/12)$ ?

Question

1604 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-09-30T07:14:05

The vector is $=-(sqrt2+sqrt6)hati+(sqrt6-sqrt2)hatj$

If the polar coordinates of the vector are $(r,theta)$ , then

The components are $(rcostheta,rsintheta)$ in the rectangular cordinates are

$x=rcosthetahati$

$y=rsinthetahatj$

Here, we have

$(r,theta)=(4,11/12pi)$

$x=4cos(11/12pi)=4cos(2/3pi+1/4pi)$

$=4(cos(2/3pi)cos(1/4pi)-sin(2/3pi)sin(1/4pi))$

$=4(-1/2*sqrt2/2-sqrt3/2*sqrt2/2)$

$=-4/4(sqrt2+sqrt6)$

$=-(sqrt2+sqrt6)$

$y=4sin(11/12pi)=4sin(2/3pi+1/4pi)$

$=4(sin(2/3pi)*cos(1/4pi)+cos(2/3pi)*sin(1/4pi))$

$=4*(sqrt3/2*sqrt2/2-1/2*sqrt2/2)$

$=(sqrt6-sqrt2)$

The vector is

$=-(sqrt2+sqrt6)hati+(sqrt6-sqrt2)hatj$

What are the components of the vector between the origin and the polar coordinate (4, (11pi)/12)(4, (11pi)/12)?