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**Gitano** 1. f(x)= x+2cosx

2. f(x)= x+2sinx

3. f(x)= e^x (sinx)

Regarding problem number 1, I know that the derivative is 1-2sinx, then when I set it equal to zero I get sinx=1/2. Therefor it would be pi/6, but the answer key says that the answer is 2npi + pi/6, 2npi + 5pi/6. I need some clarification on how to reach that conclusion.

This is just trigonometry: $\displaystyle \color{red}\sin x=\sin (\pi-x)\, \mbox{so}\,\sin x=\frac{1}{2}\Longrightarrow x=\frac{\pi}{6}+2n\pi$

$\displaystyle \color{red}\mbox{or}\,\, x=\pi-\frac{\pi}{6}+2n\pi=\frac{5\pi}{6}+2n\pi$

Remember that both basic trigonometry functions $\displaystyle \sin x\, \mbox{and} \cos x$ have period $\displaystyle =2\pi$

For the next two problems the issue is the same, only that $\displaystyle \tan x$ has period $\displaystyle \pi$

Tonio

On problem 2, I get the answer cosx= -1/2. The answer key says that the final answer is (2n +1)pi +/- pi/3. Again I am quite sure how to reach that conclusion or final answer.

Same problem on 3. tanx= -1: What would my next step be to solve the problem.

Any feedback or help would be appreciated. These problems have been bugging me all day.