Which of the following pairs of polar coordinates represents the same point in the polar plane as $\left(-3, \frac{\pi}{3}\right)$?

A) $\left(3, \frac{\pi}{3}\right)$

B) $\left(3, \frac{2\pi}{3}\right)$

C) $\left(-3, \frac{4\pi}{3}\right)$

D) $\left(3, \frac{4\pi}{3}\right)$

Which pair of coordinates represents the Cartesian point $(-2\sqrt{3}, 2)$ in polar form $(r, \theta)$, where $r > 0$ and $0 \le \theta < 2\pi$?

A) $\left(4, \frac{5\pi}{6}\right)$

B) $\left(4, \frac{11\pi}{6}\right)$

C) $\left(4, \frac{2\pi}{3}\right)$

D) $\left(16, \frac{5\pi}{6}\right)$

Math · Functions & Trigonometry · Math · Polar, Parametric & Vectors

5 Math practice questions on Polar coordinates. Questions that assess core concepts and understanding.

1.
Which of the following polar equations is equivalent to the Cartesian equation $x^2 - y^2 = 9$ ?
- A) $r^2\sin(2\theta) = 9$
- B) $r^2 = 9\cos\theta$
- C) $r\cos(2\theta) = 3$
- D) $r^2\cos(2\theta) = 9$
2.
What is the distance between the points $P\left(3, \frac{\pi}{4}\right)$ and $Q\left(5, \frac{7\pi}{12}\right)$ in the polar plane?
- A) 7
- B) $\sqrt{34}$
- C) $2\sqrt{7}$
- D) $\sqrt{19}$
3.
Which of the following Cartesian equations is equivalent to the polar equation $r = 8\sin\theta$ ?
- A) $(x - 4)^2 + y^2 = 16$
- B) $x^2 + (y + 4)^2 = 16$
- C) $x^2 + (y - 4)^2 = 16$
- D) $x^2 + y^2 = 64$
4.
Which of the following pairs of polar coordinates represents the same point in the polar plane as $\left(-3, \frac{\pi}{3}\right)$ ?
- A) $\left(3, \frac{\pi}{3}\right)$
- B) $\left(3, \frac{2\pi}{3}\right)$
- C) $\left(-3, \frac{4\pi}{3}\right)$
- D) $\left(3, \frac{4\pi}{3}\right)$
5.
Which pair of coordinates represents the Cartesian point $(-2\sqrt{3}, 2)$ in polar form $(r, \theta)$ , where $r > 0$ and $0 \le \theta < 2\pi$ ?
- A) $\left(4, \frac{5\pi}{6}\right)$
- B) $\left(4, \frac{11\pi}{6}\right)$
- C) $\left(4, \frac{2\pi}{3}\right)$
- D) $\left(16, \frac{5\pi}{6}\right)$