mathmari said:It is the straight line that passes through the origin $O$ and makes an angle of $-\frac{\pi}{6}$ with the polar axis.
A polar equation is a mathematical representation of a curve or shape in the polar coordinate system. In this system, points are described using a distance from the origin and an angle from a reference line, rather than using x and y coordinates.
To plot a polar equation, you can use a graphing calculator or manually plot points by substituting values of theta into the equation and converting them to Cartesian coordinates. Alternatively, you can use the symmetry and periodicity of polar equations to plot points in one quadrant and then reflect or rotate them to complete the graph.
θ = −pi/6 represents an angle of -π/6 radians or -30 degrees. This means that for every value of r (distance from the origin), the point will lie on a line that makes a -30 degree angle with the reference line.
The shape of a curve can be determined by analyzing the values of r in relation to theta. If r is a constant value, the curve will be a line. If r is a function of theta, the curve will be a spiral. If r is a combination of sine or cosine functions, the curve will be a rose curve or a cardioid shape.
Yes, a polar equation can be converted to a Cartesian equation. This can be done by using the equations x = r cosθ and y = r sinθ to replace r and θ in the polar equation. The resulting equation will be in the form of y = f(x), which can be plotted on a Cartesian coordinate system.