Question

Express 22∠-30 in rectangular notation.Question 1 options:(3.39, 21.74)(19.05, 11)(3.39, -21.74)(19.05, -11)

Answer 1

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:

`(19.05,-11)`