what is the period of the function ( y = - 2cos(3pi x + 1) )? write an exact, simplified answer.

Explanation:

Step1: Recall the formula for the period of a cosine function

The general form of a cosine function is (y = A\cos(Bx - C)+D), and its period is given by (T=\frac{2\pi}{|B|}).

Step2: Identify the value of (B) in the given function

For the function (y=-2\cos(3\pi x + 1)), comparing with the general form, we have (B = 3\pi).

Step3: Calculate the period

Substitute (B = 3\pi) into the period formula (T=\frac{2\pi}{|B|}). Since (|B|=3\pi), then (T=\frac{2\pi}{3\pi}). Simplify the fraction (\frac{2\pi}{3\pi}=\frac{2}{3}).

Answer:

(\frac{2}{3})