Coordinates where gradient is zero of trig functions

May 2017
9
0
uk
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 a moderator:

skeeter

Math Team
Jul 2011
3,196
1,724
Texas
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 a moderator:
  • Like
Reactions: 1 person
May 2017
9
0
uk
Think I just get 0,0 by doing that.
 
Last edited by a moderator:

skeeter

Math Team
Jul 2011
3,196
1,724
Texas
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 a moderator:

skipjack

Forum Staff
Dec 2006
21,296
2,375
$\cos(2\theta) = 0$ directly implies that $2\theta = \pi/2 + k\pi$.
 

Country Boy

Math Team
Jan 2015
3,261
899
Alabama
Think I just get 0,0 by doing that.
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 \(\displaystyle \frac{\pi}{2}\).