Topics
Complex Numbers
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India
Class XI

Graph Polar Equations

Lesson
Practice

Interactive practice questions

Consider the point $\left(8,\frac{11\pi}{6}\right)$(8,11π6​), in polar coordinates.

a

This point is $\editable{}$ units away from the pole on a polar grid.

b

What is the size of the angle that the point makes with the polar axis? Give your answer in radians.

c

Which of the following shows the location of $\left(8,\frac{11\pi}{6}\right)$(8,11π6​) on a polar grid?

A polar coordinate grid with several blue points labeled from A to H. The grid has concentric circles increasing in radius at consistent intervals which represents the axes of the polar coordinate grid. The fifth circle is labeled $10$10 indicating that it is the 10th axis. Point $A$A is at $\left(8,\frac{\pi}{3}\right)$(8,π3​); point $B$B is at $\left(8,\frac{\pi}{6}\right)$(8,π6​); point $C$C is at $\left(8,\frac{11\pi}{6}\right)$(8,11π6​); point $D$D is at $\left(8,\frac{5\pi}{3}\right)$(8,5π3​); point $E$E is at $\left(4,\frac{\pi}{3}\right)$(4,π3​); point $F$F is at $\left(4,\frac{\pi}{6}\right)$(4,π6​); point $G$G is at $\left(4,\frac{11\pi}{6}\right)$(4,11π6​); point $H$H is at $\left(4,\frac{5\pi}{3}\right)$(4,5π3​). The coordinates of all points are not explicitly given in the image and should never be given as answer to any questions/prompts.
Easy
1min

Consider the point $\left(8,\left(-30\right)^\circ\right)$(8,(−30)°), in polar coordinates.

Easy
< 1min

Consider the points that have been graphed on the polar grid below.

Easy
8min

Convert the point $\left(8,9\right)$(8,9) from rectangular coordinates to polar coordinates $\left(r,\theta\right)$(r,θ), where $0^\circ\le\theta<360^\circ$0°≤θ<360°. Give each value correct to two decimal places.

Easy
2min
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Outcomes

11.A.CNQE.1

Need for complex numbers, especially √-1, to be motivated by inability to solve every quadratic equation. Brief description of algebraic properties of complex numbers. Argand plane and polar representation of complex numbers. Statement of Fundamental Theorem of Algebra, solution of quadratic equations in the complex number system.

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