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Convert the following point from polar to Cartesian coordinates. Write the exact answer as an ordered pair. Do not round.(4.5%)

Convert The Following Point From Polar To Cartesian Coordinates Write The Exact Answer As An Ordered Pair Do Not Round45 class=

Sagot :

Solution:

Given:

[tex]\begin{gathered} (4,\frac{7\pi}{4}) \\ where; \\ r=4 \\ \theta=\frac{7\pi}{4} \end{gathered}[/tex]

To convert from polar to cartesian coordinates,

[tex]\begin{gathered} x=rcos\theta \\ y=rsin\theta \end{gathered}[/tex][tex]\begin{gathered} x=4cos\frac{7\pi}{4} \\ x=\frac{4\sqrt{2}}{2} \\ x=2\sqrt{2} \end{gathered}[/tex][tex]\begin{gathered} y=4sin\frac{7\pi}{4} \\ y=4(\frac{-\sqrt{2}}{2}) \\ y=-2\sqrt{2} \end{gathered}[/tex]

Hence, the pair as a cartesian coordinate as an ordered pair is;

[tex](2\sqrt{2},-2\sqrt{2})[/tex]

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