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Find the amplitude and period of the function, and sketch its graph. y = cos 2x

User Kadrian
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Final answer:

The amplitude of the function y = cos 2x is 1, and the period is \( \pi \) radians. The graph peaks and troughs at each interval of \( \pi \), oscillating between +1 and -1.

Step-by-step explanation:

Finding Amplitude and Period of a Cosine Function

To find the amplitude and period of the cosine function y = cos 2x, we need to understand the general form of a cosine function, which is y = A cos(Bx - C) + D, where:

  • A is the amplitude
  • B determines the period
  • C is the phase shift
  • D is the vertical translation

In the function y = cos 2x, A is implicitly 1 (since it is not written), meaning the amplitude is 1. The period can be found using the relationship T = \( \frac{2\pi}{B} \), where T is the period and B is the coefficient of x. In this case, B is 2, so the period is T = \( \frac{2\pi}{2} \) = \pi.

The graph of y = cos 2x will have peaks and troughs at intervals of \( \pi , oscillating between the values of +1 and -1, since the amplitude is 1. The graph repeats its form every period T, which, for our function, is every \( \pi radians along the x-axis.

User Almaz
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