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Hate Number Theory

Member

Registered: 2015-12-22

Posts: 11

2 trig problems

The graph of the equation

is an ellipse with center [ma­th]h,k)[/ma­th], horizontal axis length [ma­th]2a[/ma­th], and vertical axis length [ma­th]2b[/ma­th]. Find parametric equations whose graph is an ellipse with center [ma­th](h,k)[/ma­th], horizontal axis length[ma­th]2a[/ma­th], and vertical axis length [ma­th]2b[/ma­th], and explain why your answer is correct.

Let [ma­th]\mathcal{G}[/ma­th] be the graph of the parametric equations
[ma­th]\begin{align*}
x &= \cos(4t),\\
y &= \sin(6t).
\end{align*}[/ma­th]
What is the length of the smallest interval [ma­th]I[/ma­th] such that the graph of these equations for all [ma­th]t\in I[/ma­th] produces the entire graph [ma­th]\mathcal{G}[/ma­th]?

Last edited by Hate Number Theory (2016-02-02 15:21:22)

Nehushtan

Member

Registered: 2013-03-09

Posts: 957

Re: 2 trig problems

You copied and pasted the word math from my other post. Type out the word yourself on your keyboard, don't copy and paste!

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Relentless

Member

Registered: 2015-12-15

Posts: 631

Re: 2 trig problems

That's a potentially annoying bug. I tried to type it out for you

The graph of the equation

is an ellipse with center

, horizontal axis length

, and vertical axis length

. Find parametric equations whose graph is an ellipse with center

, horizontal axis length

, and vertical axis length

, and explain why your answer is correct.
Let

be the graph of the parametric equations

What is the length of the smallest interval

such that the graph of these equations for all

produces the entire graph

?

Last edited by Relentless (2016-02-02 22:15:35)

Nehushtan

Member

Registered: 2013-03-09

Posts: 957

Re: 2 trig problems

It isn't a bug. In my post in the other thread I used an invisible hyphen in the word (so the phrase [ma­th]...[/math] would not get turned into

on posting). Hate Number Theory inadvertently copied the invisible hyphen and posted it here. If only people would stop being lazy and type out words instead of using copy & paste. I mean, what's so difficult about typing just four letters on the keyboard?

Also it seems the LaTeX package in the forum software doesn't understand the \begin{align*} command. Instead of

\begin{align*}
x &= \cos(4t),\\
y &= \sin(6t).
\end{align*}

try \begin{array}:

\begin{array}{rcl}
x &=& \cos(4t),\\
y &=& \sin(6t).
\end{array}

[list=*]
[*]

[/*]
[/list]
The software doesn't understand \implies or \iff either, forcing the use of \Rightarrow and \Leftrightarrow instead.

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thickhead

Member

Registered: 2016-04-16

Posts: 1,086

Re: 2 trig problems

is well known.

Last edited by thickhead (2016-04-19 21:00:01)

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