Warning: Illegal string offset 'html' in /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php on line 909

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 114

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 127

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 136

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 137

Warning: Cannot modify header information - headers already sent by (output started at /home/hsn/public_html/forum/cache/skin_cache/cacheid_1/skin_topic.php:909) in /home/hsn/public_html/forum/admin/sources/classes/output/formats/html/htmlOutput.php on line 141
Trigonometry - HSN forum

Jump to content


Trigonometry

Started by Nathan, Mar 12 2006 12:52 PM

8 replies to this topic

#1 Nathan

    Fully Fledged Genius

  • Members
  • PipPipPipPipPipPipPip
  • 1,736 posts
  • Location:Aberdeen, Scotland
  • Gender:Male

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

    HSN Legend

  • Members
  • PipPipPipPipPipPipPipPip
  • 2,477 posts
  • Location:Paisley
  • Interests:I'm me, I guess. I wear glasses, have short spiked hair, about 5ft 9 (I think). I left fifth year of school in 2005 and is currently unemployed. I used to go to Strathclyde University to do MEng Chemical Engineering, but I hated the course, so I quit. I've started doing MSc Mathematics, from September 2006, as I have a keen (almost unhealthy) interest in Mathematics, and its applications.<br /><br />The grades I achieved in the exams:<br /><br />1 - Standard Grade Mathematics<br />1 - Standard Grade Physics<br />1 - Standard Grade Chemistry<br />1 - Standard Grade Computing Studies<br />1 - Standard Grade Craft and Design<br />2 - Standard Grade English<br />2 - Standard Grade Geography <br /><br />A (Band 1) - Higher English<br />A (Band 1) - Higher Mathematics<br />A (Band 2) - Higher Chemistry<br />B (Band 3) - Higher Physics<br /><br />Anything else ya wanna know about me, PM me or add me to your MSN contact list and chat to me there. :P
  • Gender:Male

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.

IPB Image

IPB Image
University of Strathclyde Homepage

CPU-Z snapshot
CPU-Z snapshot after OC
3D Mark 2006 results
3D Mark 2006 results after OC
3D Mark 2003 Results
3D Mark 2003 results after OC

#3 Steve

    Top of the Class

  • Admin
  • PipPipPipPipPip
  • 435 posts
  • Location:Edinburgh
  • Gender:Male

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.
HSN contribute: Help the site grow!

Looking for a Maths tutor in West Lothian? Just PM me!

#4 The Wedge Effect

    HSN Legend

  • Members
  • PipPipPipPipPipPipPipPip
  • 2,477 posts
  • Location:Paisley
  • Interests:I'm me, I guess. I wear glasses, have short spiked hair, about 5ft 9 (I think). I left fifth year of school in 2005 and is currently unemployed. I used to go to Strathclyde University to do MEng Chemical Engineering, but I hated the course, so I quit. I've started doing MSc Mathematics, from September 2006, as I have a keen (almost unhealthy) interest in Mathematics, and its applications.<br /><br />The grades I achieved in the exams:<br /><br />1 - Standard Grade Mathematics<br />1 - Standard Grade Physics<br />1 - Standard Grade Chemistry<br />1 - Standard Grade Computing Studies<br />1 - Standard Grade Craft and Design<br />2 - Standard Grade English<br />2 - Standard Grade Geography <br /><br />A (Band 1) - Higher English<br />A (Band 1) - Higher Mathematics<br />A (Band 2) - Higher Chemistry<br />B (Band 3) - Higher Physics<br /><br />Anything else ya wanna know about me, PM me or add me to your MSN contact list and chat to me there. :P
  • Gender:Male

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
IPB Image

IPB Image
University of Strathclyde Homepage

CPU-Z snapshot
CPU-Z snapshot after OC
3D Mark 2006 results
3D Mark 2006 results after OC
3D Mark 2003 Results
3D Mark 2003 results after OC

#5 Nathan

    Fully Fledged Genius

  • Members
  • PipPipPipPipPipPipPip
  • 1,736 posts
  • Location:Aberdeen, Scotland
  • Gender:Male

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

    HSN Legend

  • Members
  • PipPipPipPipPipPipPipPip
  • 2,477 posts
  • Location:Paisley
  • Interests:I'm me, I guess. I wear glasses, have short spiked hair, about 5ft 9 (I think). I left fifth year of school in 2005 and is currently unemployed. I used to go to Strathclyde University to do MEng Chemical Engineering, but I hated the course, so I quit. I've started doing MSc Mathematics, from September 2006, as I have a keen (almost unhealthy) interest in Mathematics, and its applications.<br /><br />The grades I achieved in the exams:<br /><br />1 - Standard Grade Mathematics<br />1 - Standard Grade Physics<br />1 - Standard Grade Chemistry<br />1 - Standard Grade Computing Studies<br />1 - Standard Grade Craft and Design<br />2 - Standard Grade English<br />2 - Standard Grade Geography <br /><br />A (Band 1) - Higher English<br />A (Band 1) - Higher Mathematics<br />A (Band 2) - Higher Chemistry<br />B (Band 3) - Higher Physics<br /><br />Anything else ya wanna know about me, PM me or add me to your MSN contact list and chat to me there. :P
  • Gender:Male

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.
IPB Image

IPB Image
University of Strathclyde Homepage

CPU-Z snapshot
CPU-Z snapshot after OC
3D Mark 2006 results
3D Mark 2006 results after OC
3D Mark 2003 Results
3D Mark 2003 results after OC

#7 Steve

    Top of the Class

  • Admin
  • PipPipPipPipPip
  • 435 posts
  • Location:Edinburgh
  • Gender:Male

Posted 12 March 2006 - 01:19 PM

Yes, but your second y-coordinate is wrong! (It's a minimum remember.)
HSN contribute: Help the site grow!

Looking for a Maths tutor in West Lothian? Just PM me!

#8 The Wedge Effect

    HSN Legend

  • Members
  • PipPipPipPipPipPipPipPip
  • 2,477 posts
  • Location:Paisley
  • Interests:I'm me, I guess. I wear glasses, have short spiked hair, about 5ft 9 (I think). I left fifth year of school in 2005 and is currently unemployed. I used to go to Strathclyde University to do MEng Chemical Engineering, but I hated the course, so I quit. I've started doing MSc Mathematics, from September 2006, as I have a keen (almost unhealthy) interest in Mathematics, and its applications.<br /><br />The grades I achieved in the exams:<br /><br />1 - Standard Grade Mathematics<br />1 - Standard Grade Physics<br />1 - Standard Grade Chemistry<br />1 - Standard Grade Computing Studies<br />1 - Standard Grade Craft and Design<br />2 - Standard Grade English<br />2 - Standard Grade Geography <br /><br />A (Band 1) - Higher English<br />A (Band 1) - Higher Mathematics<br />A (Band 2) - Higher Chemistry<br />B (Band 3) - Higher Physics<br /><br />Anything else ya wanna know about me, PM me or add me to your MSN contact list and chat to me there. :P
  • Gender:Male

Posted 12 March 2006 - 01:21 PM

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

IPB Image
University of Strathclyde Homepage

CPU-Z snapshot
CPU-Z snapshot after OC
3D Mark 2006 results
3D Mark 2006 results after OC
3D Mark 2003 Results
3D Mark 2003 results after OC

#9 Nathan

    Fully Fledged Genius

  • Members
  • PipPipPipPipPipPipPip
  • 1,736 posts
  • Location:Aberdeen, Scotland
  • Gender:Male

Posted 12 March 2006 - 01:23 PM

yeah, oops!

(i did have -5 on my written copy though)
Back to Problem Questions


1 user(s) are reading this topic

0 members, 1 guests, 0 anonymous users

  1. HSN forum
  2. → Higher
  3. → Mathematics
  4. → Problem Questions