What is the polar form of ( - 2 , 3 ) ?

Ayaan Barr

Ayaan Barr

Answered

2022-07-09

What is the polar form of ( - 2 , 3 ) ?

Answer & Explanation

Charlize Manning

Charlize Manning

Expert

2022-07-10Added 12 answers

Step 1
To solve 1. we use Pythagoras Theorem
r = ( - 2 ) 2 + 3 2
= 13
To solve 2. we first find the quadrant that the point lies in.
y is positive while x is negative quadrant II
Then we find the basic angle by taking inverse tangent of | y x |
α = tan - 1 ( | 3 - 2 | )
= tan - 1 ( 3 2 )
The angle that we are looking for would be
θ = π - α
= π - tan - 1 ( 3 2 )
2.16
Therefore, the polar coordinate is ( 13 , π - tan - 1 ( 3 2 ) )
Note that the answer above is not unique. You can add any integer multiples of 2 π to θ to get other representations of the same point.

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