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December 22nd, 2017, 02:10 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 08:07 AM. 
December 22nd, 2017, 06:39 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,755 Thanks: 1405  Set each derivative equal to zero and solve for $\theta$.
Last edited by skipjack; December 23rd, 2017 at 08:08 AM. 
December 23rd, 2017, 04:07 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 08:08 AM. 
December 23rd, 2017, 07:46 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,755 Thanks: 1405  $t =\cos{\theta}$ $\dfrac{dt}{d\theta} = \sin{\theta} = 0 \implies \theta = k\pi \, , \, k \in \mathbb{Z}$  $z = \sin(2\theta)$ $\dfrac{dz}{d\theta} = 2\cos(2\theta) = 2(2\cos^2{\theta}  1) = 0 \implies \cos{\theta} = \pm \dfrac{1}{\sqrt2}$ so, $\theta = \, ?$ Last edited by skipjack; December 23rd, 2017 at 08:11 AM. 
December 23rd, 2017, 08:19 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 19,059 Thanks: 1619 
$\cos(2\theta) = 0$ directly implies that $2\theta = \pi/2 + k\pi$.

February 15th, 2018, 11:13 AM  #6 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,197 Thanks: 872  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 $\displaystyle \frac{\pi}{2}$. 

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coordinates, functions, gradient, trig 
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