Question 1210421
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Consider the trigonometric function f(t) = 2 + 3 sin(4π(t − 1)).
(a) What is the amplitude of f(t)?
(b) What is the period of f(t)?
(c) What are the maximum and minimum values attained by f(t)?
(d) Sketch the graph of f(t) for t ∈ [−1, 1].
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<pre>
If a trigonometric function is given in the form

    f(t) = a + b*sin(c(t-d)),


where  c > 0, then

    - the midline ("the axis") is y = a;

    - the amplitude is  |b|;

    - the period is  {{{2pi/c}}};

    - the shift is  'd'  units to the right, if  d >= 0, and/or  |d|  units to the left, if  d < 0,

          comparing to the parent function f(t) = a + b*sin(ct).


Therefore, in this case

    (a)  the amplitude is 3 units.

    (b)  the period is  {{{2pi/4pi}}} = {{{1/2}}} = 0.5.

    (c)  the maximum is  2 + 3 = 5;  the minimum is 2 - 3 = -1.

    (d)  To plot the function, go to website https://www.desmos.com/calculator/
         and use free of charge plotting tool there.
     
         Print the formula  and get the plot immediately.
</pre>

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