document.write( "Question 262174: I have this problem and need the solution and an explanation for it:\r
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document.write( "0°<=[theta]<360°+cot[theta]=-1.4176[theta]=x\r
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document.write( " {problem in brackets}\r
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document.write( "The written form was this:\r
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document.write( "\"If 0deg <= [theta] <360deg and cot[theta] = -1.4176 then determine [theta] to the nearest tenth\".\r
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document.write( "Thank you, Steven\r
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Algebra.Com's Answer #193151 by Theo(13342)![]() ![]() You can put this solution on YOUR website! working from the written statement, I get this:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "\"If 0deg <= [theta] <360deg and cot[theta] = -1.4176 then determine [theta] to the nearest tenth\".\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "what they are saying is that the angle is between 0 and 360 degrees.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "they are also saying that tangent of the angle = -1.4176.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "if you find the angle whose tangent is -1.4176, then you have found the angle they are looking for.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "using your scientific calculator, you find the arctangent of -1.4176.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "on my calculator that equals -54.8001834 degrees.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "that would be in the 4th quadrant.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "to find the equivalent positive angle, you add 360 to it to get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "angle equals 305.1998166 degrees.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "put that angle in your calculator and get the tangent of it.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you get:\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "tangent of 305.1998166 degrees = -1.4176.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "since that's where we started from, you're good.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "basically you had 2 requirements.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you needed to find the angle whose cotangent was equal to -1.4176.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "you needed to find the equivalent angle that was between 0 and 360 degrees.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "any angle plus or minus 360 degrees is equivalent to the same angle.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "0 is equivalent to 360 is equivalent to 720, etc.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "if the angles are equivalent, then their trigonometric functions are also equivalent.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "tan(-55) = tan(-55 + 360) = tan(305).\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "here's a tutorial you may be interested in to understand this better.\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "http://www.algebra.com/algebra/homework/playground/lessons/THEO-20091204.lesson\r \n" ); document.write( "\n" ); document.write( " \n" ); document.write( " |