Answer:
True
Step-by-step explanation:
Polar Coordinates
One point in the plane can be expressed as its rectangular coordinates (x,y). Sometimes, it's convenient to express the points in the plane in polar coordinates [tex](r,\theta)[/tex], where r is the radius or the distance from the point to the origin, and [tex]\theta[/tex] is the angle measured from the positive x-direction counterclockwise.
The conversion between rectangular and polar coordinates are
[tex]r=\sqrt{x^2+y^2}[/tex]
[tex]\displaystyle tan\theta=\frac{y}{x}[/tex]
The angle can be computed as the inverse tangent of y/x and it can be negative. It's enough that x and y have opposite signs to make the angle negative. For example, if x=1, y=-1
[tex]\displaystyle tan\theta=\frac{-1}{1}=-1[/tex]
The angle that complies with the above equation is
[tex]\displaystyle \theta=-\frac{\pi}{4}[/tex]
But it can also be expressed as
[tex]\displaystyle \theta=\frac{7\pi}{4}[/tex]
Can the angle be negative? it depends on what is the domain given for [tex]\theta[/tex]. Usually, it's [tex](0,2\pi)[/tex] in which case, the angle cannot be negative.
But if the domain was [tex](-\pi,\pi)[/tex], then our first solution is valid and the angle is negative. We'll choose the most general answer: True
