ACT Math: Find the Period of f(x) = -3 sin(4π/5 x - π/2) + 6

Exact Question Text

What is the period of the trigonometric function $f(x) = -3\sin\left(\frac{4\pi}{5}x - \frac{\pi}{2}\right) + 6$?

Step-by-Step Solution

1. Identify $B$ in Standard Form $f(x) = A\sin(Bx - C) + D$:

$$ B = \frac{4\pi}{5} $$

1. Apply the Period Formula:

$$ \text{Period} = \frac{2\pi}{B} = \frac{2\pi}{\frac{4\pi}{5}} = 2\pi \times \frac{5}{4\pi} = \frac{5}{2} = \mathbf{2.5} $$