SOLUTION: 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 val

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  ;

    - 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   =  = 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.