1 Answer

Matt Byrne · Answer 1 · 2023-02-25T15:15:22+0000

To convert polar form to rectangular we can use the formula:

$A\angle\theta=A(\cos \theta+i\sin \theta)$

We have A = 22 and θ = -30, therefore

$A\angle\theta=22(\cos (-30\degree)+i\sin (-30\degree))$

Remember that

$\begin{gathered} \cos (-30\degree)=\frac{\sqrt[]{3}}{2}_{} \\ \\ \sin (-30\degree)=-(1)/(2)_{} \end{gathered}$

Therefore

$\begin{gathered} 22(\cos (-30\degree)+i\sin (-30\degree))=22(\frac{\sqrt[]{3}}{2}-(i)/(2)) \\ \end{gathered}$

Simplifying

$\begin{gathered} 22(\frac{\sqrt[]{3}}{2}-(i)/(2))=11\, \sqrt[]{3}-11i \\ \\ \end{gathered}$

We can approximately say that

$11\sqrt[]{3}=19.05$

Hence.

$22\angle-30\degree=19.05-11i$

Final answer:

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