Question

Someone pleaseee help meee!!!

Answer 1

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 $(r,\theta)$, where r is the radius or the distance from the point to the origin, and $\theta$ is the angle measured from the positive x-direction counterclockwise.

The conversion between rectangular and polar coordinates are

$r=\sqrt{x^2+y^2}$

$\displaystyle tan\theta=\frac{y}{x}$

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

$\displaystyle tan\theta=\frac{-1}{1}=-1$

The angle that complies with the above equation is

$\displaystyle \theta=-\frac{\pi}{4}$

But it can also be expressed as

$\displaystyle \theta=\frac{7\pi}{4}$

Can the angle be negative? it depends on what is the domain given for $\theta$. Usually, it's $(0,2\pi)$ in which case, the angle cannot be negative.

But if the domain was $(-\pi,\pi)$, then our first solution is valid and the angle is negative. We'll choose the most general answer: True