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blondinia [14]
3 years ago
11

Convert the rectangular coordinates (-9, 3V3) into polar form. Express the angle

Mathematics
1 answer:
Whitepunk [10]3 years ago
7 0

Answer:

(6\sqrt{3},\,\frac{5\pi}{6})

Step-by-step explanation:

The radius  r  can be found from the relationship

 r^2=x^2+y^2\\r^2=(-9)^2+(3\sqrt{3})^2\\r^2=81+27=108\\r=\sqrt{108}\\r=6\sqrt{3}

The point is in Quadrant II (-, +), so use the inverse cosine function to find the angle.

\cos{\theta}=\frac{x}{r}=\frac{-9}{6\sqrt{3}}\\\cos{\theta}=-\frac{9}{6\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}}\\\cos{\theta}=-\frac{9\sqrt{3}}{6\cdot3}\\\cos{\theta}=-\frac{\sqrt{3}}{2}\\\\\cos^{-1}\frac{-\sqrt{3}}{2}}=\frac{5\pi}{6}

See the attached image.

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