Which of the following is another representation of the polar coordinate -9, -90 degrees?
Is it 9,270 degrees
(-9,-90°)
this would point you clockwise 90° or 270° using the standard rotation.
You would then go in the opposite direction for 9 units
so equivalent to (9, 90°)
(9,270°) would be the same as (9, -90°)
To find the representation of the polar coordinate -9, -90 degrees in another form, we can use the following formula:
$\theta = \theta + 360^\circ$
where $\theta$ is the angle in degrees.
In this case, the given angle is -90 degrees. Adding 360 degrees to -90 degrees gives us:
$\theta = -90^\circ + 360^\circ$
$\theta = 270^\circ$
So, the polar coordinate -9, -90 degrees can be represented as 9, 270 degrees.
To determine if 9, 270 degrees is another representation of the polar coordinate -9, -90 degrees, we need to understand the conversion between the polar and Cartesian coordinate systems.
In the polar coordinate system, a point is represented by its distance from the origin (r) and the angle formed by the positive x-axis and the line connecting the point and the origin (θ).
To convert from polar coordinates to Cartesian coordinates, we use the following formulas:
x = r * cos(θ)
y = r * sin(θ)
Given the polar coordinates -9, -90 degrees, we can substitute these values into the formulas:
x = -9 * cos(-90)
y = -9 * sin(-90)
Evaluating these expressions:
x = -9 * cos(-90) = -9 * 0 = 0
y = -9 * sin(-90) = -9 * (-1) = 9
So, the Cartesian coordinates corresponding to the polar coordinates -9, -90 degrees are (0, 9).
Now, let's evaluate the polar coordinates 9, 270 degrees and convert them to Cartesian coordinates:
x = 9 * cos(270)
y = 9 * sin(270)
Evaluating these expressions:
x = 9 * cos(270) = 9 * 0 = 0
y = 9 * sin(270) = 9 * (-1) = -9
So, the Cartesian coordinates corresponding to the polar coordinates 9, 270 degrees are (0, -9).
From the calculations, we can see that the Cartesian coordinates for the polar coordinates -9, -90 degrees are (0, 9), while the Cartesian coordinates for the polar coordinates 9, 270 degrees are (0, -9). Therefore, 9, 270 degrees is not another representation of the polar coordinate -9, -90 degrees.