Consider the curve; r = 8 − 5 cos(θ), (−π≤ θ ≤π) given in polar coordinates. (i) Create a table with the values of the function r(θ) on [−π, π] rounded to two decimal places with step π/12 (ii) (a) Download the image file Polar coords graph paper.png with the polar coordinate graph paper from the assignment page, and open the file in any graphics editor (e.g. MS Paint). (b) Use your graphics editor to plot all the points with polar coordinates (r(θ), θ) you have found in (i) on the polar coordinate graph paper. (c) Draw a smooth curve through the plotted points, thereby getting a sketch of the curve (please proceed exactly as instructed, your solution won’t be accepted, otherwise; in particular, any image files in your solution that are not based on the above-mentioned image file will be ignored). (d) Save your work, and include the image file in your solution. (iii) Find the area of the region enclosed by the curve. Please give a complete solution to the problem.
Consider the curve;
r = 8 − 5 cos(θ), (−π≤ θ ≤π) given in polar coordinates.
(i) Create a table
with the values of the function r(θ) on [−π, π] rounded to two decimal places with step π/12
(ii) (a) Download the image file Polar coords graph paper.png with the polar coordinate graph paper from the assignment page, and open the file in any graphics editor (e.g. MS Paint).
(b) Use your graphics editor to plot all the points with polar coordinates (r(θ), θ) you have found in (i) on the polar
coordinate graph paper.
(c) Draw a smooth curve through the plotted points, thereby getting a sketch of the curve (please proceed exactly as instructed, your solution won’t be accepted, otherwise; in particular, any image files in your solution that are not based on the above-mentioned image file will be ignored).
(d) Save your work, and include the image file in your solution.
(iii) Find the area of the region enclosed by the curve.
Please give a complete solution to the problem.
Step by step
Solved in 5 steps with 18 images
