document.write( "Question 720143: please help me solve the following trigonometric equation using Pythagorean identity formula:\r
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Algebra.Com's Answer #852505 by ikleyn(53427) $\"\"$ $\"About$

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\n" ); document.write( "please help me solve the following trigonometric equation using Pythagorean identity formula:\r
\n" ); document.write( "\n" ); document.write( "1 - sin^2theta = 0.5
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\n" ); document.write( "\n" ); document.write( "        The solution in the post by @Theo is incomplete, and therefore incorrect.\r
\n" ); document.write( "\n" ); document.write( "        I came to provide a correct solution.\r
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\n" ); document.write( "\n" ); document.write( "        I will look for solutions in the interval [0°,360°), which represents the unit circle.\r
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document.write( "I will use the letter t to represent .\r\n" );
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document.write( "The Pythagorean identify is sin^2(t) + cos^2(t) = 1.\r\n" );
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document.write( "You can write it in the form\r\n" );
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document.write( "    cos^2(t) = 1 - sin^2(t).\r\n" );
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document.write( "You are given that  1 - sin^2(t) = 0.5.\r\n" );
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document.write( "Hence,\r\n" );
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document.write( "    cos^2(t) = 0.5.\r\n" );
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document.write( "Take the square root of both sides of this equation to get:\r\n" );
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document.write( "    cos(t) = +/- .\r\n" );
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document.write( "If  cos(t) = + ,  then angle  't'  is either   45°  or -45°,  which geometrically is the same as 315°.\r\n" );
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document.write( "If  cos(t) = - ,  then angle  't'  is either  135°  or  225°.\r\n" );
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document.write( "Thus, in the interval  [0°,360°)  the given equation   = 0.5  has 4 (four) solutions\r\n" );
document.write( "      that are  45°,  135°,  225°  and  315°.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved.\r
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\n" ); document.write( "\n" ); document.write( "If a student losing the roots while solving such equation, as tutor @Theo did,
\n" ); document.write( "it is considered as a grave sin. The score is cut, and the student is sent for re-training.\r
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\n" ); document.write( "\n" ); document.write( "And such teaching as presented in the post by @Theo is considered as unsatisfactory.\r
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