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

Question

1940 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-08-08T01:45:00

$-(9sqrt2)/2hati + (9sqrt2)/2hatj$

What we'll do first is find the rectangular form of the given polar coordinate, using the equations

$ul(x = rcostheta$

$ul(y = rsintheta$

where in this case

So we have

$x = 9cos((3pi)/4) = -(9sqrt2)/2$

$y = 9sin((3pi)/4) = (9sqrt2)/2$

SInce the vector starts at the origin, these values are the $x$ - and $y$ -components of the vector, so we can write the vector as

$color(blue)(ulbar(|stackrel(" ")(" "< -(9sqrt2)/2, (9sqrt2)/2 >" ")|)$

Or

$color(blue)(ulbar(|stackrel(" ")(" "-(9sqrt2)/2 hati + (9sqrt2)/2 hatj" ")|)color(white)(aa)$ (unit vector notation)

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