Convert theta=225degrees
A y=-1
B y=1
C y=x
D y=-x
E x=-1
To rectangular form
tan225° = 1
tanθ = y/x
so, y/x = 1
y=x
To convert the angle θ = 225 degrees to a Cartesian coordinate system, we need to determine the corresponding values of x and y.
First, let's visualize the angle θ = 225 degrees. This angle lies in the third quadrant of the Cartesian plane.
In the third quadrant, the x-coordinate (x-value) is negative, and the y-coordinate (y-value) is also negative.
To find the values of x and y, we can use the formulas:
x = cos(θ)
y = sin(θ)
Using a calculator or trigonometric table, we find:
x = cos(225°) ≈ -0.707
y = sin(225°) ≈ -0.707
Therefore, the coordinates in the Cartesian plane corresponding to θ = 225 degrees are approximately (-0.707, -0.707).
Now, let's check which option matches these coordinates:
A) y = -1: This option does not match, as the y-coordinate is approximately -0.707.
B) y = 1: This option does not match, as the y-coordinate is approximately -0.707.
C) y = x: This equation represents a line passing through the origin with a slope of 1. It does not match the coordinates (-0.707, -0.707), where y is not equal to x.
D) y = -x: This equation represents a line passing through the origin with a slope of -1. It matches the coordinates (-0.707, -0.707), where y is equal to -x. Therefore, this option matches our coordinates.
E) x = -1: This equation represents a vertical line passing through x = -1. It does not match the coordinates (-0.707, -0.707), where x is not equal to -1.
Hence, the correct option is D) y = -x.