My Math Forum Coordinates where gradient is zero of trig functions
 User Name Remember Me? Password

 Calculus Calculus Math Forum

 December 22nd, 2017, 03:10 AM #1 Newbie   Joined: May 2017 From: uk Posts: 9 Thanks: 0 Coordinates where gradient is zero of trig functions Hi everyone, I have two questions I am struggling with. They are: work out the coordinates when the gradient of these functions is equal to zero t=cos(theta) and Z=sin(2theta) I think I need to find the derivatives, but then what? Thanks in advance; have a nice day. Last edited by skipjack; December 23rd, 2017 at 09:07 AM.
December 22nd, 2017, 07:39 AM   #2
Math Team

Joined: Jul 2011
From: Texas

Posts: 2,691
Thanks: 1350

Quote:
 Originally Posted by DomB Hi everyone, I have two questions I am struggling with. They are: work out the coordinates when the gradient of these functions is equal to zero t=cos(theta) and Z=sin(2theta) I think I need to find the derivatives, but then what?
Set each derivative equal to zero and solve for $\theta$.

Last edited by skipjack; December 23rd, 2017 at 09:08 AM.

 December 23rd, 2017, 05:07 AM #3 Newbie   Joined: May 2017 From: uk Posts: 9 Thanks: 0 Think I just get 0,0 by doing that. Last edited by skipjack; December 23rd, 2017 at 09:08 AM.
December 23rd, 2017, 08:46 AM   #4
Math Team

Joined: Jul 2011
From: Texas

Posts: 2,691
Thanks: 1350

Quote:
 Originally Posted by DomB Think I just get 0,0 by doing that.
$t =\cos{\theta}$

$\dfrac{dt}{d\theta} = -\sin{\theta} = 0 \implies \theta = k\pi \, , \, k \in \mathbb{Z}$

------------------------------------------------------------------

$z = \sin(2\theta)$

$\dfrac{dz}{d\theta} = 2\cos(2\theta) = 2(2\cos^2{\theta} - 1) = 0 \implies \cos{\theta} = \pm \dfrac{1}{\sqrt2}$

so, $\theta = \, ?$

Last edited by skipjack; December 23rd, 2017 at 09:11 AM.

 December 23rd, 2017, 09:19 AM #5 Global Moderator   Joined: Dec 2006 Posts: 18,408 Thanks: 1459 $\cos(2\theta) = 0$ directly implies that $2\theta = \pi/2 + k\pi$.

 Tags coordinates, functions, gradient, trig

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post DomB New Users 1 December 22nd, 2017 08:18 AM vizzy22 Calculus 9 September 8th, 2017 04:23 AM IneedofHelp Trigonometry 1 October 17th, 2011 03:38 AM Ndjs Algebra 1 June 13th, 2011 06:38 AM Ndjs Elementary Math 0 December 31st, 1969 04:00 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top

Copyright © 2018 My Math Forum. All rights reserved.