Answer:
<em>True</em>
Step-by-step explanation:
<u>Polar Coordinates</u>
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
, where r is the radius or the distance from the point to the origin, and
is the angle measured from the positive x-direction counterclockwise.
The conversion between rectangular and polar coordinates are
![r=\sqrt{x^2+y^2}](https://tex.z-dn.net/?f=r%3D%5Csqrt%7Bx%5E2%2By%5E2%7D)
![\displaystyle tan\theta=\frac{y}{x}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20tan%5Ctheta%3D%5Cfrac%7By%7D%7Bx%7D)
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
![\displaystyle tan\theta=\frac{-1}{1}=-1](https://tex.z-dn.net/?f=%5Cdisplaystyle%20tan%5Ctheta%3D%5Cfrac%7B-1%7D%7B1%7D%3D-1)
The angle that complies with the above equation is
![\displaystyle \theta=-\frac{\pi}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta%3D-%5Cfrac%7B%5Cpi%7D%7B4%7D)
But it can also be expressed as
![\displaystyle \theta=\frac{7\pi}{4}](https://tex.z-dn.net/?f=%5Cdisplaystyle%20%5Ctheta%3D%5Cfrac%7B7%5Cpi%7D%7B4%7D)
Can the angle be negative? it depends on what is the domain given for
. Usually, it's
in which case, the angle cannot be negative.
But if the domain was
, then our first solution is valid and the angle is negative. We'll choose the most general answer: True