Find all points on the curve below at which the tangent line is horizontal. y = (cos x) / (2 + sin x)
can somebody help me to solve this question?
what?
$\displaystyle -2 \sin 2 - 1 \ne 0$
and $\displaystyle -2 \sin \frac 12 - 1 \ne 0$
you have a trig equation here. the x's will be angles, and you will have infinitely many answers, not just 2
as i said, you need to solve $\displaystyle -2 \sin x - 1 = 0 \implies \sin x = - \frac 12$
what $\displaystyle x$'s does that happen for?
EDIT: I'm going to bed, so i won't be able to answer you if you respond, so i'll just give you the answers.
$\displaystyle x = \frac {7 \pi}6 + 2n \pi$ for $\displaystyle n \in \mathbb{Z}$ or $\displaystyle x = \frac {11 \pi}6 + 2k \pi$ for $\displaystyle k \in \mathbb{Z}$