Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

I would appreciate help finding the answer to this question :]. Again the question is,

Find all the points on the graph of the function:

$f(x)= 2 \sin(x) + \sin^2(x)$

the second trig function is supposed to be sin squared of x but not sure how to make that on here...

at which the tangent line is horizontal.

share|improve this question
    
You might find this useful if you're curious how to use math font on MSE: MathJax Primer –  gnometorule Feb 20 '13 at 4:31
    
Awesome! Thank you! :] –  bkaifos15 Feb 20 '13 at 4:32
1  
The tangent is horizontal if and only if $f'(x)=$? –  1015 Feb 20 '13 at 4:33
    
What I posted is the entire question...it doesn't ask/say anything else. –  bkaifos15 Feb 20 '13 at 4:36
    
That's why we are asking you, what do you know about when the graph of a function is horizontal? –  Gerry Myerson Feb 20 '13 at 5:01

1 Answer 1

We can calculate $$f'(x)=2\cos(x)+2\sin(x)\cos(x)=2\cos(x)(1+\sin(x)).$$ Now, the tangent is horizontal whenever $f'(x)=0$, so this means when $$2\cos(x)=0\quad\text{or}\quad1+\sin(x)=0.$$ Solving the cosine equation gives $x=\pi/2+k\pi$ for $k\in\Bbb Z$ while solving the sine equation gives $-\pi/2+2k\pi$. Since the solution for the sine equation is actually contained in the set of solutions for the cosine equation, we can write our final answer as $x=\pi/2+k\pi$ for $k\in\Bbb Z$.

share|improve this answer
    
+1 nice/leading one. –  B. S. Feb 20 '13 at 4:56

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.