To convert the Cartesian equation y = 7 into its polar form, we start by recalling the relationship between Cartesian and polar coordinates. In polar coordinates, the connections are defined as follows:
- x = r * cos(θ)
- y = r * sin(θ)
In the given equation, we can substitute for y using the polar equivalent:
y = r * sin(θ)
Substituting this into the original equation yields:
r * sin(θ) = 7
To isolate r, we can rearrange the equation:
r = rac{7}{sin(θ)}
This is our polar equation! It expresses the relationship in terms of r and θ. The form shows that for each angle θ, the distance r from the origin is given by the equation.
Additionally, you will notice that this equation represents a horizontal line where the value of y remains constant at 7 in Cartesian coordinates, which corresponds to all the points that are at a constant distance vertically along that line in the polar coordinate system.
Thus, the polar equation for the curve represented by the Cartesian equation y = 7 is:
r = rac{7}{sin(θ)}
Feel free to explore different values for θ to visualize how this curve behaves in polar coordinates!