What is the polar form of <mstyle displaystyle="true"> ( - 11

Summer Bradford

Summer Bradford

Answered question

2022-06-28

What is the polar form of ( - 11 , 24 ) ?

Answer & Explanation

Trey Ross

Trey Ross

Beginner2022-06-29Added 30 answers

Step 1
The radius is given by the Pythagorean Theorem as
XXX r = ( - 11 ) 2 + 24 2 = 597
tan ( θ ) = 24 - 11
Unfortunately, arctan , the inverse of tan ( θ ) is by definition an angle
( - π 2 , + π 2 )
(i.e. in QI or Q IV)
In the diagram above, the angle returned by arctan ( - 24 11 ) is shown as θ 2
Taking arctan ( 24 - 11 ) = arctan ( - 24 11 )
gives us an angle that is "pi" radians less than the true value of θ
Therefore θ = π + arctan ( - 24 11 )
( r , θ ) = ( 597 , π + arctan ( - 24 11 ) )
(using a calculator)
XXX ( 24.4 , 2.0 ) ( 24.4 , 114.6 )

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