Question

What are the components of the vector between the origin and the polar coordinate `(14, (11pi)/6)`?

Answer 1

`(x,y) = ( 7 sqrt{3}, -7 )`

Explanation:

Oh my, it's like trig only has two triangles. Every one of these problems will be a variant of `30^circ` or `45^circ.` This one's `30^circ.`

`(x,y) = (r cos theta, r sin theta)`

`= (14 cos( {11 pi}/6 ) , 14 sin( {11 pi}/6 ) )`

`= ( 14 cos(pi/6), - 14 sin(pi/6) )`

`= (14 (sqrt{3}/2), -14 (1/2) )`

`= ( 7 sqrt{3}, -7 )`