Question #e3529

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Question #e3529

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Answer 1 · 2017-03-12T16:23:21

$x = \pm \frac{2}{3} k π$ $x = pm 2/3 k pi$ for $k = 0, 1, 2, \dots$ $k =0,1,2,cdots$

Explanation:

$sin (2 x) = - sin x = sin (- x)$ $sin(2x)=-sinx = sin(-x)$ then

$2 x = - x \pm 2 k π$ $2x=-xpm 2kpi$ and

$x = \pm \frac{2}{3} k π$ $x = pm 2/3 k pi$ for $k = 0, 1, 2, \dots$ $k =0,1,2,cdots$

Answer 2 · 2017-03-12T22:49:24

$x = k π$ $x = kpi$ , and
$x \pm \frac{2 π}{3} + 2 k π$ $x +- (2pi)/3 + 2kpi$

Explanation:

sin x + 2sin 2x = 0
sin x + 2sin x.cos x = 0
sin x(1 + 2cos x) = 0
a. sin x = 0 --> unit circle gives 3 solutions -->
x = 0, $x = π$ $x= pi$ , and $x = 2 π$ $x = 2pi$
b. 1 + 2cos x = 0
$cos x = - \frac{1}{2}$ $cos x = - 1/2$
Trig table of special arcs and unit circle give -->
$x = \pm \frac{2 π}{3}$ $x = +- (2pi)/3$
General answers
$x = k π$ $x = kpi$ , and
$x = \pm \frac{2 π}{3} + 2 k π$ $x = +- (2pi)/3 + 2kpi$

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Question #e3529

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