What are the components of the vector between the origin and the polar coordinate $(2, \frac{π}{6})$ $(2, pi/6)$ ?

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Answer 1 · 2017-02-06T02:52:28

See explanation.

If the polar coordinates of P are $(r, θ)$ $(r, theta)$ and O is the origin, the

Cartesian coordinates of P are $(x, y) = (r cos θ, r sin θ)$ $(x, y) = (rcostheta, rsintheta)$ .

If $\to i and \to j$ $veci and vecj$ are unit vectors in the directions Ox and Oy, then

$- - \to O P = x \to i + y \to j = (r cos θ) \to i + (r sin θ) \to j$ $vec(OP) = xveci+yvecj=(rcostheta)veci+(rsintheta)vecj$ .

Conveniently, this is presented in the component-coordinate form as

$- - \to O P = < x, y > = < r cos θ, r sin θ > or r < cos θ, sin θ >$ $vec(OP) = < x, y> = < rcostheta, rsintheta> or r < costheta, sintheta>$

What are the components of the vector between the origin and the polar coordinate (2, pi/6)(2,π6)(2, pi/6)?