What is the polar form of <mstyle displaystyle="true"> ( - 3 ,

orlovskihmw 2022-07-07 Answered
What is the polar form of ( - 3 , 4 ) ?
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Answers (1)

Madden Luna
Answered 2022-07-08 Author has 9 answers
Step 1
If ( a , b ) is a are the coordinates of a point in Cartesian Plane, u is its magnitude and α is its angle then ( a , b ) in Polar Form is written as ( u , α ) .
Magnitude of a cartesian coordinates ( a , b ) is given by a 2 + b 2 and its angle is given by tan - 1 ( b a )
Let r be the magnitude of ( - 3 , 4 ) and θ be its angle
Magnitude of ( - 3 , 4 ) = ( - 3 ) 2 + 4 2 = 9 + 16 = 25 = 5 = r
Angle of ( - 3 , 4 ) = tan - 1 ( 4 - 3 ) = tan - 1 ( - 4 3 ) = - 53.13 0
Angle of ( - 3 , 4 ) = - 53.13 0
But the given point (-3,4) is in second quadrant so we have to add 180 0 in the angle.
Angle of ( - 3 , 4 ) = - 53.13 0 + 180 0 = 126.87 0 = θ
( - 3 , 4 ) = ( r , θ ) = ( 5 , 126.87 0 )
( - 3 , 4 ) = ( 5 , 126.87 0 )
Note that the angle is given in degree measure.

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