What are the components of the vector between the origin and the polar coordinate (2,13π12)?

1 Answer
Narad T.
Dec 15, 2017

The vector is =<−(√2+√6)2,(√2−√6)2>

Explanation:

To convert from polar coordinates (r,θ) to rectangular coordinates , we apply the following equations

x=rcosθ

y=rsinθ

Here,

The polar coordinates are

r=2

and

θ=1312π

Therefore,

The rectangular coordinates are

x=2cos(1312π)=2cos(13π+34π)=2(cos(13π)cos(34π)−sin(13π)sin(34π))

=2((12)⋅(−√22)−(√32)⋅(√22))

=2−√2−√64

=−√2+√62

y=2sin(1312π)=2sin(13π+34π)=2(sin(13π)cos(34π)+cos(13π)sin(34π))

=2((√32)⋅(−√22)+(12)⋅(√22))

=2√2−√64

=√2−√62

Finally,

The vector is =<−(√2+√6)2,(√2−√6)2>

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