While this is of course true, we find that it obscures the idea of trying to represent the same graph in two different coordinate systems, and students tend to focus only on the procedure instead of the larger goal. Other students use the conversion formula tan θ=y/x and then plug in the angle of π/3 and solve for y. We talk about the fact that rise/run is simply the ratio of the opposite over the adjacent side, which can be found by taking the tangent of the angle. We talk about how we are used to writing lines in y=mx+b form, and then we go about finding the y-intercept (0) and the slope. plot points, visualize algebraic equations, add sliders, animate graphs. They recognize that the set of these points represents the graph of the equation and it is a line passing through the origin that makes a 60˚ angle with the x-axis/polar axis. graphs, and more.This worksheet will help with Piecewise functions. b) Set up an expression with two or more integrals to find. Use your calculator to solve your equation and find the polar coordinates of the point(s) of intersection. a) Set up an equation to find the value of for the intersection(s) of both graphs. I like to have students graph the set of points where the angle is π/3, regardless of what the radius is. The figure to the left shows the graphs of r 6 sin and r 3 3 cos for 0 2. Many just gave the ordered pair on the unit circle at that angle. We found that our students struggled most when converting polar equations like θ=π/3 into rectangular. As time permits, allow students time to work on homework or other practice problems in their small groups, applying their new strategies. An important take-away is that equations can be manipulated so that they match the conversion formula, and then can be substituted for the variable in the other form. On the back of their recording sheets or in a notebook have students identify and write down the major strategies they used to match the cards. It may be helpful to have the conversion formulas up on the board or in a place that’s easily visible for students.Ī Desmos version of this card sort can be found here. Note any values of where the graph hits the origin. They will then work on the final column which requires showing algebraically why the polar and Cartesian equations are equivalent. Plot each of the following points on the graph below: (a) (r (c) (r Solution: (r (r r 8 r x2 + y 6. Additionally, give each student a recording sheet where they will keep track of their matches. Each group will need one set of cards and they will work together to find matching trios. We printed each set on a different color. Displaying all worksheets related to - Polar Coordinates. We then had each group share one response back to the whole group.įor the next activity, you will need to print the card sort that contains 6 graphs, 6 equations in rectangular coordinates and 6 equations in polar coordinates. Then we had them share their response to their group members and make any edits they wanted to make. How would you describe to them what polar points are?” First, we gave students 5 minutes of individual writing time. The area inside the region bounded by the rays a and band the curve r f(. The area of a region in polar coordinates can be found by adding up areas of innitesimal circular sectors as in Figure 2(b). We gave students the prompt: “Suppose a classmate was absent yesterday. specied in polar coordinates, it is often helpful to convert to Cartesian coordinates and proceed as in Sections 9.2 and 9.3. |\) that illustrates the action of the complex product.ġ.We spent the first ten minutes of class reviewing the big ideas from yesterday’s lesson, since it was the first day they had ever seen polar coordinates.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |