Math 234-Calculus II Summer 2020
Lab 10
1 Directions
This lab requires that you have read up to section 11.4.
Go to https://student.desmos.com and type in this lab's code: G73 H5M. If you
are having difficulty with this lab, post a question in the discussion area
below. If you answer a question, give guidance, but not the entire solution.
1.1 Problem 0
Enter your name and SFA email, I need to know who to give the grades to.
1.2 Problem 1
- Define sliders for \(C_x,C_y,R_x,R_y \in [-10,10]\).
- Define the parametric functions \(X(t) = C_x + R_x\cos(t)\) and \(Y(t) = C_y +R_y\sin(t)\).
- Plot the parameterization \((X(t),Y(t))\)for \(t \in [0,2\pi]\).
- What is the graph of this parameterization, and what do the values \(C_x,C_y,R_x,R_y\) do?
1.3 Problem 2
Find the arc length using desmos of the parameterization given in Problem 1 (use formulas given in the book or lecture, not approximations using partitions).
1.4 Problem 3
Find the surface area formed by rotating the parameterization given in Problem 1 about the \(x\)-axis (this will only work if you graph is completely above the \(x\)-axis remember).
1.5 Problem 4
Graph \(r = 4\sin(5\theta)\) and find the area of one of the petals.