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

Sattelhofsk

Sattelhofsk

Answered question

2022-06-24

What is the polar form of ( - 3 , 14 )

Answer & Explanation

Carmelo Payne

Carmelo Payne

Beginner2022-06-25Added 25 answers

Step 1
To solve 1. we use Pythagoras Theorem
r = ( - 3 ) 2 + 14 2
= 205
Step 2
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 ( | 14 - 3 | )
The angle that we are looking for would be
θ = π - α
= π - tan - 1 ( 14 3 )
1.78
Therefore, the polar coordinate is ( 205 , π - tan - 1 ( 14 3 ) )
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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