
Calculus Calculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
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: 2,780 Thanks: 1431  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: 2,780 Thanks: 1431  $t =\cos{\theta}$ $\dfrac{dt}{d\theta} = \sin{\theta} = 0 \implies \theta = k\pi \, , \, k \in \mathbb{Z}$  $z = \sin(2\theta)$ $\dfrac{dz}{d\theta} = 2\cos(2\theta) = 2(2\cos^2{\theta}  1) = 0 \implies \cos{\theta} = \pm \dfrac{1}{\sqrt2}$ 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: 19,974 Thanks: 1850 
$\cos(2\theta) = 0$ directly implies that $2\theta = \pi/2 + k\pi$.

February 15th, 2018, 12:13 PM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894  Are you just finding arcsin(0) on your calculator? You need to know more about sin(x) than that to do these problems! sin(x)= 0 for x any multiple of $\displaystyle \pi$. cos(x)= 0 for x any odd multiple of $\displaystyle \frac{\pi}{2}$. 

Tags 
coordinates, functions, gradient, trig 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Coordinates where gradient is zero for t=cos(theta)  DomB  New Users  1  December 22nd, 2017 08:18 AM 
Find the coordinates of the point(s) at which the curve has the specified gradient  vizzy22  Calculus  9  September 8th, 2017 04:23 AM 
Trig problem, product of trig functions  IneedofHelp  Trigonometry  1  October 17th, 2011 03:38 AM 
Functions Finding Gradient  Ndjs  Algebra  1  June 13th, 2011 06:38 AM 
Functions Finding Gradient  Ndjs  Elementary Math  0  December 31st, 1969 04:00 PM 