document.write( "Question 282663: Solve the equation 4sin(2theta)-3cos=0 for all values on the interval $\"%220%B0%22%3C=theta%3C%22360%B0%22\"$ . Express any non-integer answers to the nearest tenth of a degree. \n" ); document.write( "
Algebra.Com's Answer #205231 by Edwin McCravy(20059) $\"\"$ $\"About$
You can put this solution on YOUR website!
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document.write( "You left off the angle for the cosine, so I can't tell whether\r\n" );
document.write( "you meant the equation to be this: \r\n" );
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document.write( "or this:\r\n" );
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document.write( "So I'll do it both ways:\r\n" );
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document.write( "If it is the first way,\r\n" );
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document.write( "Use the identity \r\n" );
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document.write( "Factor out \r\n" );
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document.write( "Use the zero-factor principle.\r\n" );
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document.write( "Set the first factor = 0:\r\n" );
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document.write( "The only angles between 0° and 360° which have their\r\n" );
document.write( "cosine equaling to zero are 90° and 270°.  So those\r\n" );
document.write( "are two of the solutions.\r\n" );
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document.write( "Set the second factor = 0:\r\n" );
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document.write( "With a calculator we find the inverse sine of \r\n" );
document.write( "is the first quadrant angle 22.02431284°.  However the\r\n" );
document.write( "angle in the second quadrant whioch has 22.02431284° as\r\n" );
document.write( "its reference angle is 157.9756872°.\r\n" );
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document.write( "So the four solutions on the interval ,\r\n" );
document.write( "with the decimals rounded to the nearest tenth of a degree are:\r\n" );
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document.write( ", , ,  \r\n" );
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document.write( "If it was supposed to have been the second way:\r\n" );
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document.write( "Divide both sides by \r\n" );
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document.write( "Divide both sides by 4:\r\n" );
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document.write( "Use the identity \r\n" );
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document.write( "With a calculator we find the inverse tangent of \r\n" );
document.write( "is the first quadrant angle 36.86989765°.  However the\r\n" );
document.write( "angle in the third quadrant which has 36.86989765° as\r\n" );
document.write( "its reference angle is 216.8698976°.\r\n" );
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document.write( "Now since the angle is  and not just ,\r\n" );
document.write( "we must find all solutions for  in twice the interval, \r\n" );
document.write( "that is the interval , so that \r\n" );
document.write( "will be in the interval .   \r\n" );
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document.write( "So we must add 360° to each of those two values, so that when\r\n" );
document.write( "we find  by dividing by 2 we will have all the\r\n" );
document.write( "solutions in the interval .\r\n" );
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document.write( "So we have\r\n" );
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document.write( ", , , ,\r\n" );
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document.write( "Now solving for , we have:\r\n" );
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document.write( ", , , ,\r\n" );
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document.write( "Or rounded to the nearest tenth of a degree:\r\n" );
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document.write( ", , , .\r\n" );
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document.write( "Edwin
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