What is the Cartesian equivalent of polar coordinates $(7, π)$ $(7, pi)$ ?

Question

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Answer 1 · 2014-10-01T22:01:54

In this problems we know that $(r, θ) \to (7, π)$ $(r,theta)->(7,pi)$ .

We also know the following equations are used to convert polar coordinates to rectangular coordinates.

$(x, y) \to (r cos (θ), r sin (θ))$ $(x,y)->(rcos(theta),rsin(theta))$

Substitute in the values for $r$ $r$ and $θ$ $theta$

$(x, y) \to (7 cos (π), 7 sin (π))$ $(x,y)->(7cos(pi),7sin(pi))$

Remember back to the unit circle

$cos (π) = - 1$ $cos(pi)=-1$
$sin (π) = 0$ $sin(pi)=0$

Substitute in those values

$(x, y) \to (7 (- 1), 7 (0))$ $(x,y)->(7(-1),7(0))$

Simplify

$(x, y) \to (- 7, 0)$ $(x,y)->(-7,0)$

What is the Cartesian equivalent of polar coordinates (7,π)(7, pi)?