Question

How do I graph a parametric equation?
x = 3 sin3t
y = 3 cos3t

Answer 1

I'm using the calculator by graphmatica :)
http://www.graphmatica.com/

Answer 2

heeh

Answer 3

haha hello

Answer 4

one sec

Answer 5

sure thing!

Answer 6

I'm not sure of the math but you can tell this is gonna be a circle with a radius of 3 centered at the origin

Answer 7

\(\large {
\begin{cases}
x = 3 sin(3t)\to \cfrac{x}{3}=sin(3t)
\\ \quad \\
y = 3 cos(3t)\to \cfrac{y}{3}=cos(3t)
\end{cases}
\\ \quad \\
recall\implies sin^2(\theta)+cos^2(\theta)=1\qquad thus
\\ \quad \\
sin^2(3t)+cos^2(3t)=1\implies \left(\cfrac{x}{3}\right)^2+\left(\cfrac{y}{3}\right)^2=1
\\ \quad \\
\cfrac{x^2}{3^2}+\cfrac{y^2}{3^2}=1\implies x^2+y^2=3^2
}\)

Answer 8

If you use \(x=sinx\) and \(y=cosx\), square them and add then you get \(x^2+y^2=sin^2 x+cos^2 x\)
Which is \(x^2+y^2=1\)

Answer 9

1=sin^2x+cos^2x