Question

How do you add two polar forms?

Answer 1

To add vectors of the polar form,follow the steps give below:

Step 1: Convert the vectors from polar form to component from using equations given below:

$$\begin{gathered} x=\left|v\right|\cos \left(\theta \right) \\ y=\left|v\right|\sin \left(\theta \right) \end{gathered}$$

Step 2: Add the $x$ and $y$ components separately.

Step 3: The simplified values can be written as the addition of the given two vectors in polar form.

Take Example:

Add the polar vector

Step 1:

$\left(23,{200}^{\circ }\right)$ and $\left(21,{59}^{\circ }\right)$

$\begin{array}{rcl}{x}_1& =& 23\cos \left(200\right)\\ & =& 23.-0.9\end{array}$

$\Rightarrow$ $x_1=-21.6$

$\begin{array}{rcl}{x}_2& =& 21\cos \left(59\right)\\ & =& 21.0.52\end{array}$

$\Rightarrow$ $x_2=10.8$

$\begin{array}{rcl}{y}_1& =& 23\sin \left(200\right)\\ & =& 23.-0.3\end{array}$

$\Rightarrow$ $y_1=-7.9$

$$\begin{gathered} y_2=21\sin \left(59\right) \\ =21.0.9 \end{gathered}$$

$\Rightarrow$ $y_2=18.0$

Step 2: and Step 3.

$x$ Component$=-21.6+10.8$

$\mathbf{=}\mathbf{-}\mathbf{10}\mathbf{.}\mathbf{8}$

$y$ Component $=-7.9+18.0$

$\mathbf{=}\mathbf{10}\mathbf{.}\mathbf{1}$