# Thread: finding min and max coordinates within interval

1. ## finding min and max coordinates within interval

Hello, my function is x-2cos(x), derived to 1+2sin(x).
I need to find the local max and min points on the interval [0,2pi]
Solving for x (sinx=-0.5) I get -pi/6 which is outside of my interval. I therefore ignore that value. My textbook says the two values I need are 7pi/6 an 11pi/6.
My problem is I cant see how they calculated those two values.
Can someone please enlighten me !

Thanks kindly

2. ## Re: finding min and max coordinates within interval

Originally Posted by fran1942
Hello, my function is x-2cos(x), derived to 1+2sin(x).
I need to find the local max and min points on the interval [0,2pi]
Solving for x (sinx=-0.5) I get -pi/6 which is outside of my interval. I therefore ignore that value. My textbook says the two values I need are 7pi/6 an 11pi/6.
My problem is I cant see how they calculated those two values.
Can someone please enlighten me !

Thanks kindly
Hint :

$\sin \frac{\pi}{6}=\frac{1}{2} ~\text{and}~ \sin \frac{5 \pi}{6}=\frac{1}{2}$

$\sin(\pi + \alpha)=-\sin \alpha$

3. ## Re: finding min and max coordinates within interval

Sketch a graph of y=sinx and draw in the line y=-1/2. Since arc sin1/2=pi/6 you will see that the solutions in your range are pi+pi/6 and 2pi-pi/6