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?

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- Oct 21st 2007, 02:53 PMbtwest69Need help on derivatives of trignometric function
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?

- Oct 21st 2007, 03:02 PMJhevon
- Oct 21st 2007, 08:09 PMbtwest69
- Oct 21st 2007, 08:14 PMJhevon
- Oct 21st 2007, 08:52 PMbtwest69
- Oct 21st 2007, 08:57 PMJhevon
- Oct 21st 2007, 09:14 PMbtwest69
- Oct 21st 2007, 09:20 PMJhevon
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 $\displaystyle k \in \mathbb{Z}$