Question

The rectangular coordinates of a point are given. Find the polar coordinates ​(r,theta​) of this point with theta expressed in radians. Let rgreater than0 and 0 less than or equal theta less than 2pi. ​(negative 6 StartRoot 3 EndRoot​, 6​)

Answer 1

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In polar coordinates P is

P  ( 12 ; 2.618 )  

Step-by-step explanation:

The point (ectangular coordinates)  

P ( -6√3  ;   6 )       P  (  x ; y )

Polar coordinates   P ( r  ;  θ )

x = r cos θ

y = r sin θ                  r > 0    and     0  ≤ θ ≤ 2π

Then

r  =  √ (x)² + (y)²        r  =  √(36)²*3 +( 36)²       r = √144

r  =  12   (hypothenuse module always positive)

The point   P  ( -6√3  ;   6 )   is in second cuadrant  between 90° and 180°

angle between  r  and horizontal axis x  is equal to θ

tan α =  l.opp/ l.adj.    tan θ =  y/x       tan θ = - 6 /6√3

tan α = - 1/√3

Then α  =  180⁰ - 150⁰  = 30⁰  or     θ =  150⁰

to express that value in radians we have :

1 π radian      =   180⁰         ⇒   3,1416   radians  =  180⁰

                                                      x ??                  =   150⁰

x =  radians

Finally the point is   P  ( 12 ; 2.618 )