+0  
 
0
104
1
avatar

The point \((r,\theta)\) in polar coordinates is \((7,5)\) in rectangular coordinates. What is the point \(\left( 2r, \theta + \frac{\pi}{2} \right)\) in rectangular coordinates?

 Nov 15, 2019
 #1
avatar+24407 
+3

The point \((r,\theta)\) in polar coordinates is \((7,5)\) in rectangular coordinates.
What is the point \(\left( 2r, \theta + \dfrac{\pi}{2} \right)\)  in rectangular coordinates?

 

\(\begin{array}{|rcll|} \hline && \text{Set $(7,5)$ to $7+5i$ } \\\\ && \text{Rotation by } \dfrac{\pi}{2}: \qquad \times i \\ && \text{scaling} : \qquad \times 2 \\\\ && 2\times(7+5i)\times i \\ &=& 2\times(7i+5i^2) \quad | \quad i^2 = -1 \\ &=& 2\times(7i-5) \\ &=& -10+14i \\\\ && \mathbf{\left( 2r, \theta + \dfrac{\pi}{2} \right) = (-10,14)} \\ \hline \end{array}\)

 

laugh

 Nov 15, 2019

55 Online Users

avatar
avatar
avatar