express in polar form: a) 2i b) -3

a) 2i = 2 at 90 degrees 
b) -3 = 3 at 180 degrees 

:)

Find the Polar form of the Cartesian equation y=1/(2x). Express answer as r=f(theta)

 


we can write 

 
then 
 
then 
 
 

and finally 
 


:)

Show algebraically that the graph of r=2csc(theta) is the line y=2. This is in polar mode.

We can use the reciprocal identities to help us see what is going on. 

 

Therefore we can write 

 


to get y=2 

:)

Find zw and z/w.

Find zw and z/w.  Leave your answers in polar form.  

z=4(cos 50(degrees)+ i sin 50(degrees))

w=cos 340(degrees) + i sin 340(degrees)

Solution:

In 3r= sin A, r and A represent polar coordinates. Write each polar equation as an equation in rectangular coordinates (x,y)

 In 3r= sin A, r and A represent polar coordinates.  Write the polar equation as an equation in rectangular coordinates (x,y)

Solution: