document.write( "Question 75425:
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\n" ); document.write( "f(x) = 2 sin(x/4 ? ?)\r
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\n" ); document.write( "What is the amplitude of this function?\r
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\n" ); document.write( "What is the exact period of f(x) (in radians)? (Recall ? radians is equivalent to 180°; ? is obtained by entering: Pi or pi.) \n" ); document.write( "

Algebra.Com's Answer #54117 by Edwin McCravy(20056) $\"\"$ $\"About$

You can put this solution on YOUR website!

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document.write( "Meaning: The amplitude is the maximum positive number \r\n" );
document.write( "of units the graph rises above the x-axis (which is\r\n" );
document.write( "also the positive number of units it falls below the \r\n" );
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document.write( "The period of a function is the pasitive distance\r\n" );
document.write( "along the x-axis which spans one cycle of the graph.\r\n" );
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document.write( "Rule:\r\n" );
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document.write( "1. Compare graph to  to\r\n" );
document.write( "   determine A, B, and C\r\n" );
document.write( "2. Amplitude = \r\n" );
document.write( "3. Period = P = ÷\r\n" );
document.write( "4. x-coordinate of starting point for basic cycle = S = ÷ \r\n" );
document.write( "5. Mark these five points on the x-axis:\r\n" );
document.write( "   S, S+P/4, S+P/2, S+3P/4, S+P\r\n" );
document.write( "6. Plot the 5 points:\r\n" );
document.write( "   (S,0), (S+P/4,A), (S+P/2,0), (S+3P/4,-A), (S+P,0)\r\n" );
document.write( "7. Draw a smooth wave though those 5 points\r\n" );
document.write( "8. Extend graph through as many cycles in both directions\r\n" );
document.write( "   as desired.\r\n" );
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document.write( "The rule is the same for the cosine graph of \r\n" );
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document.write( "except for step 6, which is\r\n" );
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document.write( "6. Plot the 5 points:\r\n" );
document.write( "   (S,A), (S+P/4,0), (S+P/2,-A), (S+3P/4,0), (S+P,A)\r\n" );
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document.write( "-------------------------------\r\n" );
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document.write( "Consider the following function \r\n" );
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document.write( "First write it as\r\n" );
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document.write( "1. Compare graph to  and determine that\r\n" );
document.write( "   A = 2, B = 1/4, C = \r\n" );
document.write( "2. Amplitude = \r\n" );
document.write( "3. Period = P = ÷ = ÷ = · = \r\n" );
document.write( "4. x-coordinate of starting point for basic cycle = S = ÷ \r\n" );
document.write( "   = ÷ = · =  \r\n" );
document.write( "5. Mark these five points on the x-axis:\r\n" );
document.write( "   S, S+P/4, S+P/2, S+3P/4, S+P\r\n" );
document.write( "   , , , , \r\n" );
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document.write( "   They simplify to:\r\n" );
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document.write( "   , , , , \r\n" );
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document.write( " 6. Plot the 5 points:\r\n" );
document.write( "   (S,0), (S+P/4,A), (S+P/2,0), (S+3P/4,-A), (S+P,0)\r\n" );
document.write( "   which are\r\n" );
document.write( "   (4p,0), (6p,2), (8p,0), (10p,-2), (12p,0)\r\n" );
document.write( "   and have numerical values for plotting:\r\n" );
document.write( "   (12.6,0), (18.8,2), (25.1,0), (31.4,-2), (37.7,0) \r\n" );
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document.write( "7. Draw a smooth wave though those 5 points\r\n" );
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document.write( "8. Extend graph through as many cycles in both directions\r\n" );
document.write( "   as desired.\r\n" );
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document.write( "Edwin

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