Students will make connections between the Cartesian graphs of trig functions and Polar graphs involving cardioids and limacons (with and without a loop).
About the Lesson
Students will begin by plotting familiar trig functions in the form y = a + bcosx on a Cartesian grid and observing the range of the plotted functions. Then, students will observe an animation where the graphs of the trig functions they plotted will be traced as the corresponding polar equation, in the form r = a + bcos𝜃 is plotted on a polar grid. Students will make connections between what they know about graphs of trig functions and the graphs of polar equations.