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

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

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Answer 1 · 2018-02-24T17:05:09

The coordinates are

$\equiv (x, y) = \equiv (- 25 \times \frac{\sqrt{3} - 1}{2 \sqrt{2}}), (- 25 \times \frac{\sqrt{3} - 1}{2 \sqrt{2}})$ $-=(x,y)=-=(-25xx(sqrt3-1)/(2sqrt2)),(-25xx(sqrt3-1)/(2sqrt2))$

Explanation:

The polar coordinates are $(r, θ) \equiv (25, \frac{- 7 π}{12})$ $(r,theta)-=(25,(-7pi)/12)$

Comparing,

$r = 25$ $r=25$

$θ = - \frac{7 π}{12}$ $theta=-(7pi)/12$

$π^{C} = 180^{\circ}$ $pi^C=180^@$

$- \frac{7 π}{12} = - \frac{7 \times 180}{12}$ $-(7pi)/12=-(7xx180)/12$

$= - 7 \times 15 = - 105$ $=-7xx15=-105$

$x = r cos θ$ $x=rcostheta$

$r cos θ = 25 cos (- 105^{\circ})$ $rcostheta=25cos(-105^@)$
$= 25 {cos 105}^{\circ} = 25 cos (180^{\circ} - 75^{\circ})$ $=25cos105^@=25cos(180^@-75^@)$
$= 25 \times (- {cos 75}^{\circ}) = 25 \times (- \frac{\sqrt{3} - 1}{2 \sqrt{2}})$ $=25xx(-cos75^@)=25xx(-(sqrt3-1)/(2sqrt2))$
$x = - 25 \times \frac{\sqrt{3} - 1}{2 \sqrt{2}}$ $x=-25xx(sqrt3-1)/(2sqrt2)$

$y = r sin θ$ $y=rsintheta$

$r sin θ = 25 sin (- 105^{\circ})$ $rsintheta=25sin(-105^@)$
$= - 25 {sin 105}^{\circ} = - 25 sin (180^{\circ} - 75^{\circ})$ $=-25sin105^@=-25sin(180^@-75^@)$
$y = - 25 {sin 75}^{\circ} = - 25 \times \frac{\sqrt{3} + 1}{2 \sqrt{2}}$ $y=-25sin75^@=-25xx(sqrt3+1)/(2sqrt2)$
$y = - 25 \times \frac{\sqrt{3} + 1}{2 \sqrt{2}}$ $y=-25xx(sqrt3+1)/(2sqrt2)$

The coordinates are

$\equiv (x, y) = \equiv (- 25 \times \frac{\sqrt{3} - 1}{2 \sqrt{2}}), (- 25 \times \frac{\sqrt{3} - 1}{2 \sqrt{2}})$ $-=(x,y)=-=(-25xx(sqrt3-1)/(2sqrt2)),(-25xx(sqrt3-1)/(2sqrt2))$

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

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Explanation:

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What are the components of the vector between the origin and the polar coordinate (25,−7π12)(25, (-7pi)/12)?

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