The norm represents the set of all points such that [tex]x^{2}+y^{2} = 49[/tex] and the direction represents the set of all points such that [tex]\frac{\pi}{3} = \tan^{-1} \frac{y}{x}[/tex].
How to determine the components of a point in polar coordinates
Polar coordinates are described by its norm (r) and direction (θ). Let P be a point in rectangular form, that is, a point of the form P(x, y).
The norm is found by Pythagorean expression and the direction is determined by inverse trigonometric functions:
Norm
[tex]r = \sqrt{x^{2}+y^{2}}[/tex] (1)
Direction
[tex]\theta = \tan^{-1} \left(\frac{y}{x} \right)[/tex] (2)
Therefore, the norm represents the set of all points such that [tex]x^{2}+y^{2} = 49[/tex] and the direction represents the set of all points such that [tex]\frac{\pi}{3} = \tan^{-1} \frac{y}{x}[/tex].
To learn more on polar coordinates, we kindly invite to check this verified question: https://brainly.com/question/11657509
