Q. 13. - Calculus

Question

Rick wants to show that the circumference of a unit circle

is $2\pi$. He decides to use the arc length formula given in

Theorem $9.14$with the function $r=\sin \theta$ on the interval

$\left[0,2\pi \right]$and obtains $2\pi$ as the length. Explain the two mistakes

he made and how they cancelled to give the correct

answer.

Step-by-Step Solution

Answer

The mistake made by rick got canceled and gave the correct answer since he calculated the area in the interval $[0,2\pi ]$

Step 1: Given information and the objective is to find the mistake in calculation.

The polar function is $r=\sin \theta$

The curve $r=\sin \theta$ is a circle with a radius $\frac{1}{2}$

Step 2: Find the two mistakes he made and how they canceled to give the correct answer.

In the interval $[0,2\pi ]$ the polar curve traces twice.

Rick's error was erased, and the proper answer was given because he calculated the area in the interval $[0,2\pi ]$