NZ Level 8 (NZC) Level 3 (NCEA) [In development]
Graph Polar Equations
Lesson

#### Worked Examples

##### QUESTION 1

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

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

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

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

##### QUESTION 2

Convert the point $\left(9,5\right)$(9,5) from rectangular coordinates to polar coordinates $\left(r,\theta\right)$(r,θ), where $0\le\theta<2\pi$0θ<2π. Give each value correct to two decimal places.

##### QUESTION 3

Convert the point $\left(4,\left(-46\right)^\circ\right)$(4,(46)°) from polar coordinates to rectangular coordinates $\left(x,y\right)$(x,y). Give each value correct to two decimal places.

### Outcomes

#### M8-9

Manipulate complex numbers and present them graphically

#### 91577

Apply the algebra of complex numbers in solving problems