8 **Educational Content: Graphing in Polar Coordinates**### Polar Graph ExplanationAbove is a polar graph with concentric circles and radial lines marked in degrees from 0° to 360°. The circles represent constant radius values from the center, while the radial lines represent angles. This graph serves as a framework for plotting polar equations, which express points in terms of a radius \( r \) and an angle \( \theta \).### Exercises8. **Graph the Function**: - Consider the function \( r(\theta) = 4 \cos (2\theta) \) on the interval \([0, 2\pi]\). - **Questions to Explore**: - How many times does the graph pass through the origin within this interval? - How many distinct "loops" does the graph make? - **Tasks**: - Anticipate the answers using algebraic techniques or by sketching the graph manually. - Confirm your predictions using a graphing calculator or software like Desmos.9. **New Function Evaluation**: - Follow the same procedures for graphing and questioning, using the function \( r(\theta) = 4 \cos (3\theta) \).10. **Function Representation**: - **Understanding Functions**: - **(a)** In rectangular coordinates, determine if a graph represents a function. - **(b)** Investigate how to discern function representation in polar coordinates. - **(c)** Use a graphing tool (e.g., Desmos) for \( r(\theta) = 3 \cos (2.1\theta) \). Evaluate whether this graph represents a function and justify your conclusions.These exercises are designed to strengthen your understanding of graphing in polar coordinates and analyzing the resulting plots for function characteristics.

Given a function rθ=4cos2θ on the interval 0 , 2π in polar coordinate. To determine: How many times the graph passes through the origin and how many distinct loops the graph will make.Here is the graph of the given function rθ=4cos2θ on the interval 0 , 2π in the polar coordinates. From the graph, we can see that graph passes through the origin 4 times and makes 4 loops.