document.write( "Question 537174: The problem is... solve the equation on the interval 0 less than/equal to theta and 2pi is greater than theta... and the equation is 2sqrt(3) sin (4theta) = 3
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\n" ); document.write( "interval 0≤θ<2π\r
\n" ); document.write( "\n" ); document.write( "2√ 3 sin (4θ) = 3\r
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\n" ); document.write( "\n" ); document.write( "The answers that the book got were { pi/12, pi/6, 2pi/3, 7pi/6,13pi/12, 5pi/3, 19pi/12}... and I want to know how they got those answers please (step by step would be great) \r
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Algebra.Com's Answer #352763 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"0%3C=theta%3C=2pi\"$ --> $\"0%3C=4theta%3C=8pi=4%2Afull%2Aturns\"$
\n" ); document.write( " $\"2sqrt%283%29+sin+%284theta%29+=+3+\"$ --> $\"+sin+%284theta%29+=+3%2F%282sqrt%283%29%29=sqrt%283%29%2F2+\"$
\n" ); document.write( "Teachers like to give students a chart, or better yet a printed circle, with the angle measurements and exact values for sine, cosine, tangent for certain notable angles, so that number may ring a bell. You do not need to memorize them, or have the chart because they all derive from Pythagoras theorem and triangles that are half of a square or half or an equilateral triangle. However, having such a chart helps keep your calculations straight.
\n" ); document.write( "You should know that $\"4theta=pi%2F3\"$ (60 degrees) is one answer (sine and cosine of 30, 45, and 60 degrees are well known values).
\n" ); document.write( " $\"4theta=%282%2F3%29pi\"$ is another solution (180-60=120 degrees, the supplementary angle has the same sine). You find more (coterminal) solutions for $\"4theta\"$ in the next turn, and the next, and the next> You can find the coterminal $\"4theta\"$ solutions by adding to the two solutions above $\"2pi\"$ (360 degrees), $\"4pi\"$ , and $\"6pi\"$ to get a total of eight values for $\"4theta\"$ :
\n" ); document.write( " $\"%281%2F3%29pi\"$ , $\"%282%2F3%29pi\"$ , $\"%287%2F3%29pi\"$ , $\"%288%2F3%29pi\"$ , $\"%2813%2F3%29pi\"$ , $\"%2814%2F3%29pi\"$ , $\"%2819%2F3%29pi\"$ , and $\"%2820%2F3%29pi\"$ .
\n" ); document.write( "Dividing by 4, we get the values for $\"theta\"$
\n" ); document.write( " $\"%281%2F12%29pi\"$ , $\"%282%2F12%29pi=%281%2F6%29pi\"$ , $\"%287%2F12%29pi\"$ , $\"%288%2F12%29pi=%282%2F3%29pi\"$ , $\"%2813%2F12%29pi\"$ , $\"%2814%2F12%29pi=%287%2F6%29pi\"$ , $\"%2819%2F12%29pi\"$ , and $\"%2820%2F12%29pi=%285%2F3%29pi\"$ . \n" ); document.write( "

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