Write each polar equation in rectangular form if possible, or describe its shape in words if an equation is impossible.
theta = 210 degrees
Since tan(theta)=y/x,
y/x = tan210° = 1/√3
y = x/√3
To convert a polar equation to rectangular form, we need to use the relationship between polar and rectangular coordinates.
The polar equation given is θ = 210 degrees. In rectangular form, we use the coordinates (x, y). The relationship between polar coordinates (r, θ) and rectangular coordinates (x, y) is as follows:
x = r * cos(θ)
y = r * sin(θ)
Let's substitute the value of θ into the equations:
x = r * cos(210 degrees)
y = r * sin(210 degrees)
Now, we need to determine the value of r in order to find the corresponding rectangular equation. Unfortunately, the given equation only specifies the value of θ (210 degrees), but it does not provide any information about r. As a result, we cannot obtain a specific rectangular equation.
However, we can describe the shape of the equation in words. The equation θ = 210 degrees represents a half-line originating from the origin (0, 0) and extending in the direction of 210 degrees.