Question

*PLEASE GET SOMEBODY WHO KNOWS TRIGONOMETRY AND HAS EXPERTISE IN TRIGONOMETRY* Length of the rose pedals on the graph? My current high school math teacher said I did not have to round but I got a decimal answer for this problem

Answer 1

Solution

The length of a curve in polar coordinate

$\begin{gathered} L=\int_a^b\sqrt{r^2+(\frac{dr}{d\theta})^2} \\ \\ \Rightarrow\frac{dr}{d\theta}=24\cos(4\theta) \end{gathered}$

Given r = 6 sin(4 theta)

$L=\int_0^2\sqrt{36\sin^2\theta+576\cos^2(4\theta)}d\theta=$

L = 32.09