Year 11 Maths - Specialist Graphing techniques

Graphing using polar coordinates

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Questions

Question 1

58652

Using technology or otherwise, sketch the spiral with polar equation $r=\dfrac{\theta}{\pi}$ for $0 \le \theta \le 2 \pi$

Answer

Refer to worked solutions

Worked Solution

$$
\begin{aligned}
\text{when}\quad\theta&=0, r=0 \rightarrow(0,0) \\
\theta&=\frac{\pi}{2}, r=\frac{1}{2} \rightarrow\left(\frac{1}{2}, \frac{\pi}{2}\right) \\
\theta&=\pi, r=1 \rightarrow(1, \pi) \\
\theta&=\frac{3 \pi}{2}, r=1 \frac{1}{2} \rightarrow\left(1 \frac{1}{2}, \frac{3 \pi}{2}\right) \\
\theta&=2 \pi, r=2 \rightarrow(2,2 \pi)
\end{aligned}
$$

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