What is the polar form of (16, -4)?

Jaidyn Bush

Jaidyn Bush

Answered question

2022-05-26

What is the polar form of (16, -4)?

Answer & Explanation

Scarlet Reid

Scarlet Reid

Beginner2022-05-27Added 8 answers

Step 1
The quickest method is to use the formula:
( x , y ) = ( x 2 + y 2 , arctan ( y x ) )
Below is an alternative method.
x = r cos θ
y = r sin θ
16 = r cos θ
- 4 = r sin θ
Step 2
Squaring both equations:
256 = r 2 cos 2 ( θ )
16 = r 2 sin 2 ( θ )
Adding both equations:
272 = r 2 cos 2 ( θ ) + r 2 sin 2 ( θ )
272 = r 2 ( cos 2 ( θ ) + sin 2 ( θ ) )
272 = r 2 ( 1 ) r = ± 272 = ± 4 17
We only need the positive root, negative radii can exist, and a point can be represented by many different polar coordinates, unlike Cartesian coordinates which are unique.
θ = arctan ( y x ) = arctan ( - 4 16 ) = arctan ( - 1 4 ) = - 0.24498
Polar coordinate:
( 4 17 , - 0 , 245 )

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