What are the components of the vector between the origin and the polar coordinate $(25, (-7pi)/12)$ ?

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Answer 1 · 2018-02-24T17:05:09

The coordinates are

$-=(x,y)=-=(-25xx(sqrt3-1)/(2sqrt2)),(-25xx(sqrt3-1)/(2sqrt2))$

The polar coordinates are $(r,theta)-=(25,(-7pi)/12)$

Comparing,

$r=25$

$theta=-(7pi)/12$

$pi^C=180^@$

$-(7pi)/12=-(7xx180)/12$

$=-7xx15=-105$

$x=rcostheta$

$rcostheta=25cos(-105^@)$
$=25cos105^@=25cos(180^@-75^@)$
$=25xx(-cos75^@)=25xx(-(sqrt3-1)/(2sqrt2))$
$x=-25xx(sqrt3-1)/(2sqrt2)$

$y=rsintheta$

$rsintheta=25sin(-105^@)$
$=-25sin105^@=-25sin(180^@-75^@)$
$y=-25sin75^@=-25xx(sqrt3+1)/(2sqrt2)$
$y=-25xx(sqrt3+1)/(2sqrt2)$

The coordinates are

$-=(x,y)=-=(-25xx(sqrt3-1)/(2sqrt2)),(-25xx(sqrt3-1)/(2sqrt2))$

What are the components of the vector between the origin and the polar coordinate (25, (-7pi)/12)(25, (-7pi)/12)?