# What are the components of the vector between the origin and the polar coordinate (-9, (5pi)/4)?

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Aug 16, 2017

#### Answer:

The x-component and the y-component are both $\setminus \frac{9 \sqrt{2}}{2}$

#### Explanation:

To find the components of a vector given the polar coordinate creating the vector, you do the following:

$\left(r , \setminus \theta\right) \implies \left(r \cos \left(\setminus \theta\right) , r \sin \left(\setminus \theta\right)\right)$

In this case:

$\left(- 9 , \frac{5 \pi}{4}\right) \implies \left(- 9 \cos \left(\frac{5 \pi}{4}\right) , - 9 \sin \left(\frac{5 \pi}{4}\right)\right)$
$\implies \left(\setminus \frac{9 \sqrt{2}}{2} , \setminus \frac{9 \sqrt{2}}{2}\right)$

So the x-component and the y-component are both $\setminus \frac{9 \sqrt{2}}{2}$

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