Question

Graph each pair of parametric equations.

x = 3 sin3t
y = 3 cos3t

Answer 1

help any body, dont understand how to graph or where to start

Answer 2

do you have a graphing calculator?

Answer 3

i do not is there one online i can use

Answer 4

Well, you need to take some time to analyse the problem, see if you can find something familiar... in particular, what is x² ?
What is y² ?

Answer 5

here's one.

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiJ4XjIiLCJjb2xvciI6IiMwMDAwMDAifSx7InR5cGUiOjEwMDB9XQ--

Answer 6

ok so how do i plug it in the calculator

Answer 7

change the "function" to "parametric" and simply type in your equations.

Answer 8

= sin3t

y = cos3t

dx/dt = 3cos(3t) and dy/dt = -3sin(3t)

dy/dx = (dy/dt)(dt/dx) = -3sin(3t) / 1 / 3cos(3t) = - 9sin(3t)cos(3t) = - 4.5sin(6t)

when t = 2π/9. dy/dx = - 4.5sin(12π/9) = - 4.5sin(4π/3))

but x = sin(2π/3) and y = cos(2π/3) when t = 2π/9

so the line is

y - cos(2π/3) / {x - sin (2π/3)} = - 4.5sin(4π/3)

Answer 9

L = 2 ∫ √(18 - 18(cos²(t) - sin²(t))) dt, over [0, π]
L = 2 √18 ∫ √(1 - cos²(t) + sin²(t)) dt, over [0, π]
L = 2 √18 ∫ √(sin²(t) + sin²(t)) dt, over [0, π]
L = 2 √18 ∫ √(2sin²(t)) dt, over [0, π]
L = 2 √18 √2 ∫ √(sin²(t)) dt, over [0, π]
L = 2 √36 ∫ sin(t) dt, over [0, π]
L = 2(6) [-cos(t)] over [0, π]
L = 12 (-cos(π) + cos(0))
L = 12 (1 + 1)
L = 12(2)
so L= (24)

Answer 10

No, @Kuuttboylife let's not complicate life more than it should be :P
x = 3sin 3t
y = 3cos 3t
Which means
x² = 9sin² 3t
y² = 9cos² 3t

So, add them up
x² + y² = 9sin² 3t + 9cos² 3t = 9(sin² 3t + cos² 3t)
Trig identities remind us that sin² 3t + cos² 3t = 1, so...
x² + y² = 9
And I bet, that's MUCH easier to graph, @tomatooooo @TNNG ? ^.^

Answer 11

IT's 24 lol

Answer 12

well it is much more clear @Kuuttboylife

Answer 13

so i graph 9

Answer 14

NO. You graph
x² + y² = 9
Which is a....?

Answer 15

if you looking for the arc length of the curve it's 24

Answer 16

function?

Answer 17

Nope, @Kuuttboylife the arclength of this curve is not 24, but rather, the circumference of the circle
x² + y² = 9, which is
\[\large 6\pi\]

Answer 18

im sorry i graph it has a circle

Answer 19

Yep :)

Answer 20

A circle with radius... what's the radius? :)

Answer 21

ahh that make some time lol

Answer 22

but what would i do for
x = 7 sin t + sin 7t
y = 7 cos t + cos 7t

Answer 23

nevermind?

Answer 24

wait yeah how do you do that

Answer 25

Kinda reached my limit there :)

Answer 26

i feel you there thnx for you help though

Answer 27

No problem :)