## trusev1 Group Title Find all points (i.e. all x-values) between 0 and 2pi where the line tangent to the graph of y =sinx/2+cosx is horizontal one year ago one year ago

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1. tkhunny Group Title

Have you considered the 1st Derivative?

2. trusev1 Group Title

1st derivative would be -(cot x) (cosx/-sinx) how would I get the points from that?

3. tkhunny Group Title

If that is the correct 1st derivative, which I didn't check, you determine where it is zero.

4. trusev1 Group Title

well the derivative of sinx is cosx and the derivative of any constant is always 0 and the derivative of cosx is -sinx and we know that cotx =cosx/sinx

5. trusev1 Group Title

I am not sure how I would determine where it would be zero..

6. RaphaelFilgueiras Group Title

horizontal tg = 0(no variation)

7. tkhunny Group Title

No. That will not do. You need the Quotient Rule. I get the 1st Derivative as $$\dfrac{2\cos(x)+1}{(2+\cos(x))^{2}}$$. After that, simply concern yourself with the numerator being zero, unless the denominator happens to be zero in the same place.

8. tkhunny Group Title

This assumes your original expression was $$\dfrac{\sin(x)}{2+\cos(x)}$$. Was it?

9. RaphaelFilgueiras Group Title

|dw:1372217350005:dw|

10. trusev1 Group Title

yes tkhunny that was the original equation

11. tkhunny Group Title

Then I gave the correct 1st Derivative and you should use parentheses to clarify your meaning. Remember your Order of Operations.

12. tkhunny Group Title

gtg sorry.

13. trusev1 Group Title

rapahael can you still help?

14. RaphaelFilgueiras Group Title

yes

15. trusev1 Group Title

so do I need to set the numerator =0

16. RaphaelFilgueiras Group Title

yes, because if the tangent line is horizontal, his angular coefficient is zero

17. trusev1 Group Title

so then I end up with cosx=-1/2

18. RaphaelFilgueiras Group Title

yes

19. trusev1 Group Title

so is that my only x value , -1? ( my reasoning behind that is that cos of 60degrees=1/2) so then y x value is -1?

20. RaphaelFilgueiras Group Title

|dw:1372217864898:dw|

21. RaphaelFilgueiras Group Title

pi-pi/3,pi+pi/3

22. RaphaelFilgueiras Group Title

@trusev1 get it?

23. trusev1 Group Title

I get that but it is asking for the x-values that are at the line tangent is horizontal. so we got the derivative and even from your picture both those points would have the same x-value.

24. RaphaelFilgueiras Group Title

no. my figure isnt the graph of your question,it's just the trigonometric circle