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

Question

1421 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-04-24T02:16:40

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

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 $30^circ.$

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

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

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

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

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

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