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anonymous
 3 years 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
anonymous
 3 years 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

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tkhunny
 3 years ago
Best ResponseYou've already chosen the best response.1Have you considered the 1st Derivative?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.01st derivative would be (cot x) (cosx/sinx) how would I get the points from that?

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0well 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
 3 years ago
Best ResponseYou've already chosen the best response.0I am not sure how I would determine where it would be zero..

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0horizontal tg = 0(no variation)

tkhunny
 3 years ago
Best ResponseYou've already chosen the best response.1No. 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
 3 years ago
Best ResponseYou've already chosen the best response.1This assumes your original expression was \(\dfrac{\sin(x)}{2+\cos(x)}\). Was it?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1372217350005:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes tkhunny that was the original equation

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0rapahael can you still help?

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so do I need to set the numerator =0

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0yes, because if the tangent line is horizontal, his angular coefficient is zero

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so then I end up with cosx=1/2

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0so 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
 3 years ago
Best ResponseYou've already chosen the best response.0dw:1372217864898:dw

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0I 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.

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0no. my figure isnt the graph of your question,it's just the trigonometric circle
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