document.write( "Question 1199171: Find the values of θ between 0° and 180° such that 2cos 3θ =3sin 3θ \n" ); document.write( "

Algebra.Com's Answer #832898 by ikleyn(52788) $\"\"$ $\"About$

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\n" ); document.write( "Find the values of θ between 0° and 180° such that 2cos 3θ =3sin 3θ
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document.write( "We start from this given equation\r\n" );
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document.write( "    2*cos(3θ) = 3*sin(3θ).     (1)\r\n" );
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document.write( "Looking in it, we see that cos(3θ) =/= 0  (since  = 1).\r\n" );
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document.write( "Therefore, we can divide both sides by cos(3θ).  Doing so, from (1) we get\r\n" );
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document.write( "     = ,  or  tan(3θ) = .    (2)\r\n" );
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document.write( "Hence,  3θ =  = 33.69 degrees is one of several possible solutions for 3θ,\r\n" );
document.write( "which gives  θ = 33.69/3 = 11.23 degrees.\r\n" );
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document.write( "Since the tangent function is periodical with the period of 180 degrees, \r\n" );
document.write( "there are other solutions to equation (2)\r\n" );
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document.write( "    3θ = 33.69+180 = 213.69 degrees and  3θ = 33.69+360 = 393.69 degrees.    (3)\r\n" );
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document.write( "From (3), it gives two other solutions for θ in the interval  [0,180] degrees.\r\n" );
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document.write( "These two additional solutions are  213.69/3 = 71.23 degrees  and  393.69/3 = 131.23 degrees.\r\n" );
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document.write( "ANSWER.  In the given interval [0,180] degrees, there are three solutions to the given equation\r\n" );
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document.write( "         θ = 11.23 degrees;  θ = 71.23 degrees  and  θ = 131.23 degrees.\r\n" );
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