document.write( "Question 968758: Please help, I posted this question earlier only to realise I had put 1π instead of 1/2π like i should have.
\n" ); document.write( "Consider the trigonometric function f (t) = −1 + 4 sin( 1/2 π(t − 1)).
\n" ); document.write( "(a) What is the amplitude of f(t)? (b) What is the period of f(t)?
\n" ); document.write( "(c) What are the maximum and minimum values attained by f(t)? (d) Sketch the graph of f (t) for t ∈ [−1, 3]. \n" ); document.write( "

Algebra.Com's Answer #591946 by Edwin McCravy(20059) $\"\"$ $\"About$

You can put this solution on YOUR website!
f(t) = −1 + 4 sin( 1/2 π(t − 1)).
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document.write( "Rule:\r\n" );
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document.write( "For   \r\n" );
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document.write( "1. The amplitude is |A|\r\n" );
document.write( "2. The period is \r\n" );
document.write( "3. The horizontal \"phase\" shift or displacement is -C.\r\n" );
document.write( "4. The vertical shift or displacement is D.\r\n" );
document.write( "5. If A > 0, the maximum value is reached when t is such that \r\n" );
document.write( "   and the minimum value is reached when t is such that \r\n" );
document.write( "6. If A < 0, the maximum value is reached when t is such that \r\n" );
document.write( "   and the minimum value is reached when t is such that \r\n" );
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document.write( "For  \r\n" );
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document.write( "1. The amplitude is |A| = |4| = 4\r\n" );
document.write( "2. The period is \r\n" );
document.write( "3. The horizontal \"phase\" shift or displacement is -C = -(-1) = +1\r\n" );
document.write( "4. The vertical shift or displacement is D = -1\r\n" );
document.write( "5. If A > 0, the maximum value is reached when t is such that \r\n" );
document.write( "   Since 4 > 0, \r\n" );
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document.write( "                Multiply both sides by \r\n" );
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document.write( "To find that maximum value we substitute 2 for t in the\r\n" );
document.write( "original equation:\r\n" );
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document.write( "and the minimum value is reached when t is such that \r\n" );
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document.write( "   Since 4 > 0, \r\n" );
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document.write( "                Multiply both sides by \r\n" );
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document.write( "To find that minimum value we substitute 0 for t in the\r\n" );
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document.write( "The graph below shows the maximum value of 3 at t=2, and the\r\n" );
document.write( "minimum value of -5 at t=0. \r\n" );
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document.write( "The green dashed line shows the vertical displacement of -1 below the horizontal\r\n" );
document.write( "axis.  The horizontal shift was actually 1 to the right and to show the basic\r\n" );
document.write( "shifted period we would have drawn the graph on t∈[1,5] rather than for t∈[−1,3], \r\n" );
document.write( "but you were instructed to draw the graph on t∈[−1,3].  Then the minimum would \r\n" );
document.write( "have been reached at t=4 instead of t=0.  Notice that we could have used  \r\n" );
document.write( "instead of  since they are coterminal.  That would have given us t=4.\r\n" );
document.write( "TMI (i.e., Too Much Information, right? J.) \r\n" );
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document.write( "Edwin

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