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 )

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 )