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.