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13 Nov 2019
Consider the polar curve defined by r-1-sin θ over the interval [0, 2 a. Use your calculator to sketch the curve. Adjust the window size until you're sure you see all of the "interesting" features of the graph. Sketch the graph on your paper. Label both axes with a scale and make sure that all of the extrema appear. b. Use calculus to find all values ofθ where the tangent line is horizontal. c. Use calculus to find all values of θ where the tangent line is vertical. (Hint-you will need to use a trigonometric identity to solve the equation.) d. If all of your trigonometry was correct, you should find that you get one angle that is an answer to both parts b and c. Obviously, a tangent line cannot be both horizontal and vertical at the same time. Use a limit to figure out what is really going on with the tangent line at that point. e. Find the area inside the curve f. Set up the necessary integral to find the arc length between the points you found in part "b". Simplify the integrand, but do NOT evaluate the integral -just set it up
Consider the polar curve defined by r-1-sin θ over the interval [0, 2 a. Use your calculator to sketch the curve. Adjust the window size until you're sure you see all of the "interesting" features of the graph. Sketch the graph on your paper. Label both axes with a scale and make sure that all of the extrema appear. b. Use calculus to find all values ofθ where the tangent line is horizontal. c. Use calculus to find all values of θ where the tangent line is vertical. (Hint-you will need to use a trigonometric identity to solve the equation.) d. If all of your trigonometry was correct, you should find that you get one angle that is an answer to both parts b and c. Obviously, a tangent line cannot be both horizontal and vertical at the same time. Use a limit to figure out what is really going on with the tangent line at that point. e. Find the area inside the curve f. Set up the necessary integral to find the arc length between the points you found in part "b". Simplify the integrand, but do NOT evaluate the integral -just set it up
Lelia LubowitzLv2
12 Feb 2019