document.write( "Question 1117560: Solve the following trigonometric equation for 1π/6≤β<7π/4:sin(β)=−0.493
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\n" ); document.write( "can someone tell me how to do this question ? i really need to know how to do it because this one might go to the final exam, please help me ! \n" ); document.write( "

Algebra.Com's Answer #732688 by ikleyn(52794) $\"\"$ $\"About$

You can put this solution on YOUR website!
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document.write( "1.  You should understand that the solutions are in quadrants QIII and QIV.\r\n" );
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document.write( "2.  Calculate the given endpoints of the solution interval \r\n" );
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document.write( "     =  = 0.523;    =  = 5.495.\r\n" );
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document.write( "3.  Find  arcsin(0.493) = 0.516 radians (using your calculator).  It is in quadrant QI.\r\n" );
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document.write( "4.  You should understand that the solution to  sin(b) = - 0.493  is  units (half the period of sine) ahead in QIII:  \r\n" );
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document.write( "         = arcsin(0.493) +  = 0.516 + 3.14 = 3.656.\r\n" );
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document.write( "    It is still in the assigned limits.  Thus you just found the solution in QIII.\r\n" );
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document.write( "5.  Now you need to find (and to check) the solution in QIV.\r\n" );
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document.write( "    There are two ways to find it.\r\n" );
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document.write( "        a)  You can find arcsin(-0.493), using your calculator. You will get  \r\n" );
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document.write( "             = -0.516 radians.\r\n" );
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document.write( "            Add   = 6.28  (one rotation about the unit circle) to it to get QIV.\r\n" );
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document.write( "            So, your new value for  is -0.516 + 6.28 = 5.764.\r\n" );
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document.write( "            But it is greater than the limit 5.495 of the given domain, so this solution does not work.\r\n" );
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document.write( "          b)  Or, knowing the behavior of sine function,  you can find the distance from   to  :  \r\n" );
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document.write( "               =  = 1.054\r\n" );
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document.write( "              and then to add this value 1.054  to  :   = 5.764  ( ! the SAME value as you found above ! )\r\n" );
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document.write( "              It is your candidate for  ;  but it fails since it is greater than the upper boundary of  5.495.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Your analysis is completed. You just found the unique solution $\"b%5B1%5D\"$ = 3.656.\r
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\n" ); document.write( "\n" ); document.write( "So, your algorithm again:\r
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document.write( "     - Find the boundaries of the domain.\r\n" );
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document.write( "     - Think in what quadrants the solution should be.\r\n" );
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document.write( "     - Evaluate the solution using your calculator.\r\n" );
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document.write( "     - Check if it satisfies the given constraints.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Surely, you should know the behavior / (how the plots look like) for basic trigonometry functions.\r
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