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

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- tkhunny

Have you considered the 1st Derivative?

- anonymous

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

- tkhunny

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

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- anonymous

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

- anonymous

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

- anonymous

horizontal tg = 0(no variation)

- tkhunny

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.

- tkhunny

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

- anonymous

|dw:1372217350005:dw|

- anonymous

yes tkhunny that was the original equation

- tkhunny

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

- tkhunny

gtg sorry.

- anonymous

rapahael can you still help?

- anonymous

yes

- anonymous

so do I need to set the numerator =0

- anonymous

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

- anonymous

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

- anonymous

yes

- anonymous

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?

- anonymous

|dw:1372217864898:dw|

- anonymous

pi-pi/3,pi+pi/3

- anonymous

@trusev1 get it?

- anonymous

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.

- anonymous

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

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