Which equation is the polar equivalent to the equation y=−√3/3x?
A)θ=π/6
B)θ=π/3
C)θ=2π/3
D)θ=5π/6
ALL OF YOU WILL DIE XD
To determine the polar equivalent of a Cartesian equation, we need to convert the equation from Cartesian coordinates (x, y) to polar coordinates (r, θ).
The conversion from Cartesian to polar coordinates is as follows:
r = √(x^2 + y^2)
θ = arctan(y/x)
Let's apply these conversions to the given equation y = -√3/3x:
First, we square both sides of the equation:
y^2 = (√3/3x)^2
y^2 = (3/9)x^2
y^2 = (1/3)x^2
Next, we convert to polar coordinates using the conversions mentioned earlier:
r^2 = x^2 + y^2
r^2 = x^2 + (1/3)x^2
r^2 = (4/3)x^2
Now, we can compare this polar equation to the options given:
A) θ = π/6
B) θ = π/3
C) θ = 2π/3
D) θ = 5π/6
By comparing the equations, we can see that none of the given options matches the polar equation we obtained. Therefore, the answer is none of the above.
That isn’t even an option oobleck
well tanθ = y/x = -√3/3
ditch the x