How do you find all solutions for $4 sin θ cos θ = \sqrt{3}$ $4sinthetacostheta=sqrt(3)$ for the interval $[0, 2 π]$ $[0,2pi]$ ?

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How do you find all solutions for $4 sin θ cos θ = \sqrt{3}$ $4sinthetacostheta=sqrt(3)$ for the interval $[0, 2 π]$ $[0,2pi]$ ?

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Answer 1 · 2014-10-24T12:34:14

4 $sin θ cos θ$ $sin theta cos theta$ = $\sqrt[]{}$ $root$ 3
2 $sin 2 θ$ $sin2theta$ = $\sqrt[]{}$ $root$ 3
$sin 2 θ$ $sin 2theta$ = ( $\sqrt[]{}$ $root$ 3) /2

$2 θ$ $2theta$ = $n π$ $n pi$ + ${(- 1)}^{n} \frac{π}{3}$ $(-1)^n pi /3$

$θ$ $theta$ = $n \frac{π}{2}$ $n pi / 2$ + ${(- 1)}^{n} \frac{π}{6}$ $(-1)^n pi / 6$

For n=0, $θ$ $theta$ = $\frac{π}{6}$ $pi /6$

For n=1, $θ$ $theta$ = $\frac{π}{3}$ $pi /3$

For n=2, $θ$ $theta$ = $7 \frac{π}{6}$ $7 pi/ 6$

For n=3, $θ$ $theta$ = $3 \frac{π}{2}$ $3pi /2$ - $\frac{π}{6}$ $pi/6$

For n=4, $θ$ $theta$ becomes greater than $2 π$ $2pi$ .
THus the values of $θ$ $theta$ for n= 0, 1, 2, 3 are the solutions.

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How do you find all solutions for $4 sin θ cos θ = \sqrt{3}$ $4sinthetacostheta=sqrt(3)$ for the interval $[0, 2 π]$ $[0,2pi]$ ?

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How do you find all solutions for $4 sin θ cos θ = \sqrt{3}$ $4sinthetacostheta=sqrt(3)$ for the interval $[0, 2 π]$ $[0,2pi]$ ?