document.write( "Question 1210421: Consider the trigonometric function f(t) = 2 + 3 sin(4π(t − 1)).
\n" ); document.write( "(a) What is the amplitude of f(t)?
\n" ); document.write( "(b) What is the period of f(t)?
\n" ); document.write( "(c) What are the maximum and minimum values attained by f(t)?
\n" ); document.write( "(d) Sketch the graph of f(t) for t ∈ [−1, 1]. \n" ); document.write( "

Algebra.Com's Answer #852463 by ikleyn(52968) $\"\"$ $\"About$

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\n" ); document.write( "Consider the trigonometric function f(t) = 2 + 3 sin(4π(t − 1)).
\n" ); document.write( "(a) What is the amplitude of f(t)?
\n" ); document.write( "(b) What is the period of f(t)?
\n" ); document.write( "(c) What are the maximum and minimum values attained by f(t)?
\n" ); document.write( "(d) Sketch the graph of f(t) for t ∈ [−1, 1].
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document.write( "If a trigonometric function is given in the form\r\n" );
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document.write( "    f(t) = a + b*sin(c(t-d)),\r\n" );
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document.write( "where  c > 0, then\r\n" );
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document.write( "    - the midline (\"the axis\") is y = a;\r\n" );
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document.write( "    - the amplitude is  |b|;\r\n" );
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document.write( "    - the period is  ;\r\n" );
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document.write( "    - the shift is  'd'  units to the right, if  d >= 0, and/or  |d|  units to the left, if  d < 0,\r\n" );
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document.write( "          comparing to the parent function f(t) = a + b*sin(ct).\r\n" );
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document.write( "Therefore, in this case\r\n" );
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document.write( "    (a)  the amplitude is 3 units.\r\n" );
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document.write( "    (b)  the period is   =  = 0.5.\r\n" );
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document.write( "    (c)  the maximum is  2 + 3 = 5;  the minimum is 2 - 3 = -1.\r\n" );
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document.write( "    (d)  To plot the function, go to website https://www.desmos.com/calculator/\r\n" );
document.write( "         and use free of charge plotting tool there.\r\n" );
document.write( "     \r\n" );
document.write( "         Print the formula  and get the plot immediately.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved: all questions are answered and all necessary instructions are provided.\r
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