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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 December 24, 2021, 4:47 pm ad1c9bdddf
    https://brainmass.com/math/trigonometry/working-sinusoidal-function-7121

    SOLUTION This solution is FREE courtesy of BrainMass!

    (1)
    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 [3x+ pi ] Gives the answer y = 21

    Case1

    y = {3+4(sin[3x+ pi])/3} Gives the answer y = 5
    Because Sin(5pi/6)= 0.5 )

    Case2

    y = 3+4 Sin[3x+(pi/3)] Gives the answer y = 1 (One among your ans)

    Sin (3x+pi/3)= Sin(3pi/2 + pi/3) = Sin(11pi/6) = -0.5

    y = 3+ (4 x -0.5 ) = 3-2= 1

    (2)
    A periodic function can be defined as any function for which,

    f(x) = f (x + T) ......(i) for all x.

    (that is, value of the function is the same after we add another constant (T) to it)

    The smallest constant T which satisfies the above equation is called the period (or the fundamental period) of the function.

    The period of the function y = sin Ax is 2pi/A.

    Note that A = | A |

    The function's value must remain invariant as we use x in it. The smallest value of x for which the function is invariant is the period.

    This gives, x = 2(pi/3) (Answer is F)

    We need not consider other values as the only variable is x.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:47 pm ad1c9bdddf>
    https://brainmass.com/math/trigonometry/working-sinusoidal-function-7121

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