Question #7f0cc

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Question #7f0cc

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Answer 1 · 2016-10-13T14:16:50

$x = arctan (- \frac{2}{7}) + π n \approx 0.2783 + π n$ $x = arctan(-2/7)+pin ~~ 0.2783 + pin$

Explanation:

$2 cos (x) + 7 sin (x) = 0$ $2cos(x)+7sin(x)=0$

$\Rightarrow 7 sin (x) = - 2 cos (x)$ $=> 7sin(x)=-2cos(x)$

$\Rightarrow \frac{sin (x)}{cos (x)} = - \frac{2}{7}$ $=> sin(x)/cos(x) = -2/7$

$\Rightarrow tan (x) = - \frac{2}{7}$ $=> tan(x) = -2/7$

$=> x = arctan(-2/7)+pin, n in ZZ$

$~~0.2783+pin$

Note that we add $npi$ to account for $tan(x)$ being periodic with a period of $pi$ , thus $tan(arctan(-2/7)) = tan(arctan(-2/7)+pi)=tan(arctan(-2/7)+2pi) = ...$

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