If the polar coordinates of a point are 6- -3- then the Cartesian coordinates are

The correct option is D (3, 3√(3))We know the conversion formula, x = rcosθ y = rsinθ Given : r = 6, θ= π3 Now, x = 6cosπ3 = 3 y = 6sinπ3 = 3√(3) Hence, the ...

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Standard XII

Mathematics

Distance Formula

If the polar ...

Question

If the polar coordinates of a point are $(6, \frac{π}{3})$ , then the Cartesian coordinates are

(3, 1)

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(1, 3)

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(3 \sqrt{3}, 3)

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(3, 3 \sqrt{3})

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Solution

The correct option is D $(3, 3 \sqrt{3})$
We know the conversion formula,
$x = r cos θ y = r sin θ$
Given : $r = 6, θ = \frac{π}{3}$
Now, $x = 6 cos \frac{π}{3} = 3$
$y = 6 sin \frac{π}{3} = 3 \sqrt{3}$
Hence, the Cartesian coordinates are $(3, 3 \sqrt{3})$ .

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If the polar coordinates of a point are (6,π3), then the Cartesian coordinates are

The correct option is D (3,3√3)We know the conversion formula, x=rcosθy=rsinθ Given : r=6, θ=π3 Now, x=6cosπ3=3 y=6sinπ3=3√3 Hence, the Cartesian coordinates are (3,3√3).

If the polar coordinates of a point are $(6, \frac{π}{3})$ , then the Cartesian coordinates are

The correct option is D $(3, 3 \sqrt{3})$
We know the conversion formula,
$x = r cos θ y = r sin θ$
Given : $r = 6, θ = \frac{π}{3}$
Now, $x = 6 cos \frac{π}{3} = 3$
$y = 6 sin \frac{π}{3} = 3 \sqrt{3}$
Hence, the Cartesian coordinates are $(3, 3 \sqrt{3})$ .