Math 234-Calculus II Summer 2020
Lab 6
This lab is best done during/after homework for Section 8.1.
1 Directions
Go to https://student.desmos.com and type in this lab's code: HNY 8N3.
For this lab, we will pretend to not know about the constant \(\pi\), so you are not allowed to use it.
We define a new constant \(\tau\) as the ratio of the circumference of a circle over the radius of a circle, \(\tau = C/r\). Your job is to use Calculus II methods to give an approximation of \(\tau\). In problem Problem 1 you approximate \(\tau\) by performing a finite sum. In Problem 2 you approximate \(\tau\) by letting desmos evaluate an integral.
1.1 Problem 0
Enter your name and SFA email, I need to know who to give the grades to.
1.2 Problem 1
It is up to you to determine how to do this, but here are some ideas:
- You probably what to use a circle of radius 1, since then you only need to find the circumference of the circle.
- You don't need to use a full circle, a half or a quarter of a circle will do (this way you can define a function).
- You probably want to approximate the arc length of a curve using ideas from Section 8.1 and previous labs. Try cutting up the semi or half circle into segments, then summing the distance between consecutive points on the circle.
1.3 Problem 2
Use the arc length integral formula from Section 8.1 to approximate \(\tau\).