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Polar coordinates of a point are given. Find the rectangular coordinates of the point.

 

(-3, 120°)

 

(3, -135°)

 Nov 19, 2018
 #1
avatar+101431 
+1

First one

This is a little tricky.......r is always positive.....so....we need to add 180° to 120°

(-3, 120°)  =  ( 3, 300°)

 

So

 

cos 300 =  x / 3

 

3cos300 = x  

 

3 (1/2)  =  x  

 

1.5  = x

 

And

 

sin300 = y / 3

 

3sin300 = y

 

3 * -√3/2   = y  

 

-(3/2)√3   = y

 

-3√3 / 2   = y

 

So

 

(x , y )   =   ( 1.5, -3√3 / 2 )

 

 

cool cool cool

 Nov 19, 2018
 #2
avatar+101431 
+1

Second one

 

-135°   =  360 - 135   =  225°

 

So...we have   (3, 225°)

 

This one is easy.....it is a 45° angle in the 3rd Quadrant  

The sine and cosine are equal here....so the x,y coordinates will be the same

 

cos 225  =  x / 3

 

3cos 225  = x

 

3 ( -1 /√2)  = x

 

-3/√2  = x   = y

 

So

 

(x , y )   =  ( -3/√2 , -3/√2 )

 

 

 

cool cool cool

 Nov 19, 2018

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