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Trigonometry - HSN forum

# Trigonometry

8 replies to this topic

### #1Nathan

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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

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

### #2The Wedge Effect

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Posted 12 March 2006 - 01:02 PM

QUOTE(nathanm @ Mar 12 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

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:

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.

### #3Steve

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Posted 12 March 2006 - 01:05 PM

Hi,

This is a silly question . There is no need to use differentiation in this problem, as it's really only asking where .

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 .

Then you just find stationary points in the normal way, i.e. by solving . Then determine their nature.

Hope that helps .

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

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.

### #5Nathan

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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

and thanks for the diagram

### #6The Wedge Effect

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Posted 12 March 2006 - 01:19 PM

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

thanks to both of you.

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

and thanks for the diagram

Yeah, you would give your coordinates in that form.

### #7Steve

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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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### #8The 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.

### #9Nathan

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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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