Finding the critical numbers of the function.

Nicolas5150

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Jan 15, 2014
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Having a little trouble on what to do next once I have set my two equations to zero.

The original question is:

Find all the critical numbers of the function f(theta)= 2Sec(theta)+Tan(theta) , 14pi<theta<16pi

IMG_2558.jpg

So far I took the equation and found the first derivative of the function and set both values to zero which resulted in:

1/cos(theta) = 0 and then sin(theta)=-1/2

I am not really sure as what to do for my next step.

I am including a snap shot to show all of my steps to get the first derivative. If someone could assist me on what to do next it would be greatly appreciated.
 
The original question is:

Find all the critical numbers of the function f(theta)= 2Sec(theta)+Tan(theta) , 14pi<theta<16pi


So far I took the equation and found the first derivative of the function and set both values to zero which resulted in:

1/cos(theta) = 0 and then sin(theta)=-1/2

\(\displaystyle \sec (\theta ) \ne 0\) so the only possible solution is \(\displaystyle \sin (\theta ) =-\frac{1}{2}\).
 
sin(theta) = -1/2

Look at the unit circle. What values have a sin of -1/2? Add those values to 14pi to find the angles in the given interval.

If it's easier, convert the radians to degrees. Multiply by 180/pi.
 
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