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Find all points (i.e. all xvalues) between 0 and 2pi where the line tangent to the graph
of y =sinx/2+cosx is horizontal
 10 months ago
 10 months ago
Find all points (i.e. all xvalues) between 0 and 2pi where the line tangent to the graph of y =sinx/2+cosx is horizontal
 10 months ago
 10 months ago

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tkhunnyBest ResponseYou've already chosen the best response.1
Have you considered the 1st Derivative?
 10 months ago

trusev1Best ResponseYou've already chosen the best response.0
1st derivative would be (cot x) (cosx/sinx) how would I get the points from that?
 10 months ago

tkhunnyBest ResponseYou've already chosen the best response.1
If that is the correct 1st derivative, which I didn't check, you determine where it is zero.
 10 months ago

trusev1Best ResponseYou've already chosen the best response.0
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
 10 months ago

trusev1Best ResponseYou've already chosen the best response.0
I am not sure how I would determine where it would be zero..
 10 months ago

RaphaelFilgueirasBest ResponseYou've already chosen the best response.0
horizontal tg = 0(no variation)
 10 months ago

tkhunnyBest ResponseYou've already chosen the best response.1
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.
 10 months ago

tkhunnyBest ResponseYou've already chosen the best response.1
This assumes your original expression was \(\dfrac{\sin(x)}{2+\cos(x)}\). Was it?
 10 months ago

RaphaelFilgueirasBest ResponseYou've already chosen the best response.0
dw:1372217350005:dw
 10 months ago

trusev1Best ResponseYou've already chosen the best response.0
yes tkhunny that was the original equation
 10 months ago

tkhunnyBest ResponseYou've already chosen the best response.1
Then I gave the correct 1st Derivative and you should use parentheses to clarify your meaning. Remember your Order of Operations.
 10 months ago

trusev1Best ResponseYou've already chosen the best response.0
rapahael can you still help?
 10 months ago

trusev1Best ResponseYou've already chosen the best response.0
so do I need to set the numerator =0
 10 months ago

RaphaelFilgueirasBest ResponseYou've already chosen the best response.0
yes, because if the tangent line is horizontal, his angular coefficient is zero
 10 months ago

trusev1Best ResponseYou've already chosen the best response.0
so then I end up with cosx=1/2
 10 months ago

trusev1Best ResponseYou've already chosen the best response.0
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?
 10 months ago

RaphaelFilgueirasBest ResponseYou've already chosen the best response.0
dw:1372217864898:dw
 10 months ago

RaphaelFilgueirasBest ResponseYou've already chosen the best response.0
pipi/3,pi+pi/3
 10 months ago

RaphaelFilgueirasBest ResponseYou've already chosen the best response.0
@trusev1 get it?
 10 months ago

trusev1Best ResponseYou've already chosen the best response.0
I get that but it is asking for the xvalues 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 xvalue.
 10 months ago

RaphaelFilgueirasBest ResponseYou've already chosen the best response.0
no. my figure isnt the graph of your question,it's just the trigonometric circle
 10 months ago
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