We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. cookie policy and privacy policy.
 
+0  
 
0
41
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+23542 
+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

29 Online Users

avatar