What is the Cartesian form of $(5, \frac{3 π}{2})$ $(5,(3pi )/2)$ ?

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What is the Cartesian form of $(5, \frac{3 π}{2})$ $(5,(3pi )/2)$ ?

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Answer 1 · 2017-12-23T08:49:59

The cartesian point is $(0, - 5)$ $(0,-5)$ .

Explanation:

$x = r cos (θ)$ $x=rcos(theta)$ and $y = r sin (θ)$ $y=rsin(theta)$ and for the given point $r = 5$ $r=5$ and $θ = \frac{3 π}{2}$ $theta=(3pi)/2$ .

$x = 5 cos (\frac{3 π}{2}) = 5 \cdot 0 = 0$ $x=5cos((3pi)/2)=5*0=0$
$y = 5 sin (\frac{3 π}{2}) = 5 \cdot (- 1) = - 5$ $y=5sin((3pi)/2)=5*(-1)=-5$

So the cartesian point is $(0, - 5)$ $(0,-5)$ .

Answer 2 · 2017-12-23T10:41:35

$(0, - 5)$ $(0,-5)$

Explanation:

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$that is (r, θ) \to (x, y) where$ $"that is "(r,theta)to(x,y)" where"$

$∙ x x = r cos θ and y = r sin θ$ $•color(white)(x)x=rcostheta" and "y=rsintheta$

$here r = 5 and θ = \frac{3 π}{2}$ $"here "r=5" and "theta=(3pi)/2$

$\Rightarrow x = 5 \times cos (\frac{3 π}{2}) = 5 \times 0 = 0$ $rArrx=5xxcos((3pi)/2)=5xx0=0$

$\Rightarrow y = 5 \times sin (\frac{3 π}{2}) = 5 \times - 1 = - 5$ $rArry=5xxsin((3pi)/2)=5xx-1=-5$

$\Rightarrow (5, \frac{3 π}{2}) \to (0, - 5)$ $rArr(5,(3pi)/2)to(0,-5)$

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