Question

The graph of a sinusoidal function intersects its midline at (0,−3)and then has a maximum point at (2,-1.5). Write the formula of the function, where x is entered in radians. f(x)= Please answer fast

Answers

  1. The sinusoidal function that represents the graph is equal to y = 1.5 · cos (2π · t/8) – 3.

    How to derive a sinusoidal function

    In this question we must derive a sinusoidal function based on two given points. Sinusoidal functions are periodic functions that uses trigonometric functions and have the following form:
    y = A · cos (2π · x/T) + B      (1)
    Where:
    • A – Amplitude
    • T – Period
    • B – Vertical midpoint
    The horizontal distance between the midline and the maximum point is equal to a quarter of the period. Hence,
    T = 4 · (2 – 0)
    T = 8
    The vertical midpoint and amplitude of the sinusoidal function are now calculated:
    Vertical midpoint
    B = – 3
    Amplitude
    A = – 1.5 – (- 3)
    A = 1.5
    Then, the sinusoidal function that represents the graph is equal to y = 1.5 · cos (2π · t/8) – 3.
    To learn more on sinusoidal functions: https://brainly.com/question/12060967
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