Question

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Answer 1

use below to find the slope :

\[\dfrac{dy}{dx} = \dfrac{dy}{dt} / \dfrac{dx}{dt}\]

Answer 2

http://tutorial.math.lamar.edu/Classes/CalcII/ParaTangent.aspx

Answer 3

click that link for details ^

Answer 4

I kinda looked at that before but I'm confused how to find the derivative of this equation; I've never found derivatives of parametric equations before

Answer 5

easy,

x=cos(3t)

dx/dt = ?

Answer 6

-3sin(3t)?

Answer 7

yep

y=sin(5t)

dy/dt = ?

Answer 8

5cos(5t)

Answer 9

and just divide them?

Answer 10

exactly !

Answer 11

and plug in pi/9 for t, right?

Answer 12

Because that's what I'm doing

Answer 13

yes !

Answer 14

and that's just going to be the slope, okay :) how do I find the equation after though? like what formula do I have to use? Is it still point-slope? Or is that different

Answer 15

\[\dfrac{dy}{dx} = \dfrac{dy}{dt} / \dfrac{dx}{dt} = -\dfrac{5\cos (5t)}{3\sin (3t)} \]

Answer 16

plugin t = pi/9 above to get the slope at t = pi/9

Answer 17

yup, I did that and got (10sin(pi/18))/3sqrt(3)

Answer 18

yes u wil still use the same point-slope formula

Answer 19

How will I use the point slope formula with this? Since there's only one coordinate?

Answer 20

how did u get (10sin(pi/18))/3sqrt(3)

?

Answer 21

http://www.wolframalpha.com/input/?i=%285cos%285*pi%2F9%29%29%2F%28-3sin%283*pi%2F9%29%29 is this like this?

Answer 22

is it*

Answer 23

lol okay, u have simplified it...

Answer 24

yes thats ur slope,
what about point ?

Answer 25

Like, how do I plug it into the point slope formula?

Answer 26

What will the point slope formula look like for this

Answer 27

Like I know m would be the answer I got for the slope, but the other values I dont know

Answer 28

pont-slope form :
\(y - y_1 = m(x-x_1)\)

Answer 29

u already knw \(m\)

Answer 30

to get the point, plugin \(t = \frac{\pi}{9}\) in :

x=cos(3t), y=sin(5t)

Answer 31

Thanks! I got y=0.3x+0.8 for the tangent line (which I hope is correct)

Answer 32

I have to estimate it to the nearest 0.1 units

Answer 33

http://www.wolframalpha.com/input/?i=sin%285pi%2F9%29+-+%280.3cos%283pi%2F9%29%2B0.8+%29

Answer 34

not getting 0 ?

Answer 35

is that due to rounding ?

Answer 36

So I'm not sure

Answer 37

looks good :)

Answer 38

Why does wolfram alpha give a different answer though?

Answer 39

wolfram answer is same as urs

Answer 40

that link was just for checking...
ur equation was off by 0.03 which is okay since u have rounded it to 0.1

Answer 41

Oh ok, good :) thanks

Answer 42

np :)