Respuesta :

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

[tex]A\angle\theta=A(\cos \theta+i\sin \theta)[/tex]

We have A = 22 and θ = -30, therefore

[tex]A\angle\theta=22(\cos (-30\degree)+i\sin (-30\degree))[/tex]

Remember that

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

Therefore

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

Simplifying

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

We can approximately say that

[tex]11\sqrt[]{3}=19.05[/tex]

Hence.

[tex]22\angle-30\degree=19.05-11i[/tex]

Final answer:

[tex](19.05,-11)[/tex]