Question

Find the points on the curve below at which the tangent is horizontal. Use n as an arbitrary integer. (Enter your answers as a comma-separated list.)
y = sinx/(2+cosx)

Answer 1

take the derivative, set it equal to zero and solve. how far have you gotten?

Answer 2

just got the derivative which is \[y'= (2\cos(x)+1)/(\cos(x)+2)^2\]

Answer 3

looks good to me. so set
\[2\cos(x)+1=0\]
\[\cos(x)=-\frac{1}{2}\] and so we get an infinite number of possibilities for x

Answer 4

lets see if we can find a formula for them.
\[\cos(\frac{2\pi}{3})=-\frac{1}{2}\] and so one answer would be
\[\frac{2\pi}{3}+2k\pi, k \in \mathbb Z\]

Answer 5

another answer is
\[\cos(\frac{4\pi}{3})=-\frac{1}{2}\] so we could also write
\[x=\frac{4\pi}{3}+2k\pi, k \in \mathbb Z\]

Answer 6

i don't see a way to combine this into one formula, but maybe that is because i am not smart enough.