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Trigonometry - HSN forum

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Trigonometry


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#1 Nathan

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Posted 12 March 2006 - 12:52 PM

Right, i have this question, (and 5 or 6 others like it ) for tomorrow and i dont know how to do it.
anyway, its probably really simple, but the question is;

Use differentiation to show that the function f(x) = 5sin x has a maximum turning value of 5 at x=pi/2 and a minimum value of -5 at x=pi

Any help would be appreciated. Thanks smile.gif

oh, so far i have f'(x) = 5cosx

sp's occur where f'(x) = 0

=> 5cosx =0

i just dunno where to go from there

#2 The Wedge Effect

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Posted 12 March 2006 - 01:02 PM

QUOTE(nathanm @ Mar 12 2006, 12:52 PM) View Post

Right, i have this question, (and 5 or 6 others like it ) for tomorrow and i dont know how to do it.
anyway, its probably really simple, but the question is;

Use differentiation to show that the function f(x) = 5sin x has a maximum turning value of 5 at x=pi/2 and a minimum value of -5 at x=pi

Any help would be appreciated. Thanks smile.gif

oh, so far i have f'(x) = 5cosx

sp's occur where f'(x) = 0

=> 5cosx =0

i just dunno where to go from there


You solve to find x, like so:



\begin{align*}
5\cos x=0\\
\cos x=0\\
x=\frac {\pi}{2}\,or\,x=\frac {3\pi}{2}
\end{align*}

You then work out maximum and mininum SP's coordinates using these values. If you need further explanations, I'd be happy enough to help.


#3 Steve

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Posted 12 March 2006 - 01:05 PM

Hi,

This is a silly question tongue.gif . There is no need to use differentiation in this problem, as it's really only asking where \sin(x)=1.

Anyway, since you're asked to use differentiation (which you would never be in an exam btw) here's what to do. You'd look up the front of the exam and find that \frac{d}{dx}\left(5\sin(x)\right) = 5\cos(x).

Then you just find stationary points in the normal way, i.e. by solving 5\cos(x)=0. Then determine their nature.

Hope that helps smile.gif.



If you are unsure about solving trigonometric equations, the brand new notes on Trigonometry are available: Trig notes.
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#4 The Wedge Effect

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Posted 12 March 2006 - 01:08 PM

It would also help if you sketched a graph just to make things clearer.

IPB Image

Blue line is 5 Sin(x) and green line is 5 Cos(x), it helps you see where the stationary points are, and see where it's coming from when differentiating and solving.

Edit: Sorry, that's huge. Oh well, more for you to look at. tongue.gif

#5 Nathan

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Posted 12 March 2006 - 01:11 PM

thanks to both of you.

also, would you just give your co-ords in the form



\begin{align*}
(\frac {\pi}{2},5)and\,(\frac {3\pi}{2},5)
\end{align*}

and thanks for the diagram smile.gif

#6 The Wedge Effect

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Posted 12 March 2006 - 01:19 PM

QUOTE(nathanm @ Mar 12 2006, 01:11 PM) View Post

thanks to both of you.

also, would you just give your co-ords in the form



\begin{align*}
(\frac {\pi}{2},5)and\,(\frac {3\pi}{2},5)
\end{align*}

and thanks for the diagram smile.gif


Yeah, you would give your coordinates in that form.

#7 Steve

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Posted 12 March 2006 - 01:19 PM

Yes, but your second y-coordinate is wrong! (It's a minimum remember.)
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#8 The Wedge Effect

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Posted 12 March 2006 - 01:21 PM

Hmm, didn't notice that, I was just looking at the first set of coordinates. tongue.gif

#9 Nathan

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Posted 12 March 2006 - 01:23 PM

yeah, oops!

(i did have -5 on my written copy though)





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