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Q. 43

Expert-verifiedFound in: Page 567

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

In Problems 39-54,the poplar coordinates of a point are given.Find rectangular coordinates of each point.

$(6,150\xb0)$

The rectangular coordinates corresponding to the polar coordinates $(6,150\xb0)$are$(-3\sqrt{3},3)$

The given poplar coordinates of a point $(6,150\xb0)$

For a point *P* on the terminal side of $\theta $ and having polar coordinates $(r,\theta )$ , the corresponding rectangular coordinates are given by $x=r\mathrm{cos}\theta $and $y=r\mathrm{sin}\theta $ .

Substitute $6$ for $r$ and $150\xb0$ for $\theta $ in to get the value of *x* .

$x=r\mathrm{cos}\theta \phantom{\rule{0ex}{0ex}}=6.\mathrm{cos}(150\xb0)\phantom{\rule{0ex}{0ex}}=6.\left(-\frac{\sqrt{3}}{2}\right)\phantom{\rule{0ex}{0ex}}=-3\sqrt{3}$

$y=r\mathrm{sin}\theta \phantom{\rule{0ex}{0ex}}=6.\mathrm{sin}\left(150\xb0\right)\phantom{\rule{0ex}{0ex}}=6.\frac{1}{2}\phantom{\rule{0ex}{0ex}}=3$

Therefore, the rectangular coordinates corresponding to the polar coordinates $(6,150\xb0)$are $(-3\sqrt{3},3)$

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