Answer:}
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 )
