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lozanna [386]
3 years ago
13

Someone pleaseee help meee!!!

Mathematics
1 answer:
Ahat [919]3 years ago
6 0

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 (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

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