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9 December, 19:32

Find the amplitude and period of y = - 3cos (2x + 3) Use your calculator to graph the function and state its symmetry. Find the first positive x-intercept using your calculator's zero function.

I wish to know if there is a way to find the amplitude and period algebraically

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  1. 9 December, 23:08
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    The amplitude is |-3| = 3.

    The period, T, is obtained from

    (2*pi) / T = 2

    T = pi

    From the calculator, the first positive zero is approximately x = 0.85

    Algebraically:

    The cos function takes a minimum of - 1 and a maximum value of + 1.

    Therefore y can be at most - 3 or + 3.

    This makes the amplitude = 3.

    The general expression for the sinusoidal function is

    y = Acos ((2*pi) / T + b) + k

    Therefore, find T from the equation

    (2*pi) / T = 2 = > T = pi.
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