Given point M (6√3,-6), which is located on the rectangular coordinate plane, what are the representations of the point in polar form, where -2л ≤ 0 ≤ 2 л? O (124) (12.-5A) (-12-11F) (12.ZA) 6 6 6 -7)( 12, 12, })( 5 л 3 2n 3 -12,-- ) (-12.45 T 3 5T (-12, 57) (12,¹17) (12.-7)( (12--12-²) 6 6 (12-) (125-12.) (12-45) 3 3

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Given point M (6sqrt(3), -6) which is located on the rectangular coordinate plane, what are the representations of the point in polar form, where −2π ≤ θ ≤ 2 π?

Given point \( M \left( 6\sqrt{3}, -6 \right) \), which is located on the rectangular coordinate plane, what are the representations of the point in polar form, where \(-2\pi \leq \theta \leq 2\pi\)?

- \(\left( 12, \frac{\pi}{6} \right), \left( 12, -\frac{5\pi}{6} \right), \left( -12, -\frac{11\pi}{6} \right), \left( 12, \frac{7\pi}{6} \right)\)

- \(\left( 12, \frac{\pi}{3} \right), \left( 12, -\frac{5\pi}{3} \right), \left( -12, -\frac{2\pi}{3} \right), \left( -12, \frac{4\pi}{3} \right)\)

- \(\left( -12, -\frac{5\pi}{6} \right), \left( 12, \frac{11\pi}{6} \right), \left( -12, -\frac{\pi}{6} \right), \left( -12, -\frac{7\pi}{6} \right)\)

- \(\left( 12, -\frac{\pi}{3} \right), \left( 12, \frac{5\pi}{3} \right), \left( -12, -\frac{2\pi}{3} \right), \left( 12, -\frac{4\pi}{3} \right)\)
Transcribed Image Text:Given point \( M \left( 6\sqrt{3}, -6 \right) \), which is located on the rectangular coordinate plane, what are the representations of the point in polar form, where \(-2\pi \leq \theta \leq 2\pi\)? - \(\left( 12, \frac{\pi}{6} \right), \left( 12, -\frac{5\pi}{6} \right), \left( -12, -\frac{11\pi}{6} \right), \left( 12, \frac{7\pi}{6} \right)\) - \(\left( 12, \frac{\pi}{3} \right), \left( 12, -\frac{5\pi}{3} \right), \left( -12, -\frac{2\pi}{3} \right), \left( -12, \frac{4\pi}{3} \right)\) - \(\left( -12, -\frac{5\pi}{6} \right), \left( 12, \frac{11\pi}{6} \right), \left( -12, -\frac{\pi}{6} \right), \left( -12, -\frac{7\pi}{6} \right)\) - \(\left( 12, -\frac{\pi}{3} \right), \left( 12, \frac{5\pi}{3} \right), \left( -12, -\frac{2\pi}{3} \right), \left( 12, -\frac{4\pi}{3} \right)\)
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