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    Working with a sinusoidal function

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    This question concerns the function

    y/3 = 3+ 4sin [3x+ pi ]

    Where x is measured in radians.

    (1) Choose the one option which gives the value of the function when x= pi/2

    (2) Choose the one option which gives the period of the function.

    Options for questions 1 and 2.

    A 1
    B. 2
    C. 3
    D. 4
    E. pi/3
    F. 2pi/3
    G. pi
    H. 3pi

    © BrainMass Inc. brainmass.com May 24, 2023, 12:57 pm ad1c9bdddf

    Solution Preview

    our function is

    y/3 = 3+ 4sin [3x+ pi ]

    when x=pi/2

    We have, 3x + pi = (3pi/2)+pi = 5pi/2 = (2pi + pi/2)

    Sin function repeats itself when we add 2pi to it

    Hence Sin(2pi + pi/2)= Sin(pi/2) = 1

    Substitute this value back to the given function and find the value of y.

    y/3 = 3+ 4sin ...

    Solution Summary

    A thorough answer with all mathematical steps. The sinusoidal function values are examined. The period of the functions are determined.