Question

find the horizontal shift.

y = cos(5x + 2π)

? / π

enter either + or -.

Explanation:

Step1: Recall the general form

The general form of a cosine function is \( y = \cos(Bx - C) \), and the horizontal shift is \( \frac{C}{B} \). We need to rewrite the given function \( y = \cos(5x + 2\pi) \) in this form.
Rewrite \( 5x + 2\pi \) as \( 5x - (-2\pi) \), so the function is \( y = \cos(5x - (-2\pi)) \). Here, \( B = 5 \) and \( C = -2\pi \).

Step2: Calculate the horizontal shift

Using the formula for horizontal shift \( \frac{C}{B} \), substitute \( B = 5 \) and \( C = -2\pi \). So the horizontal shift is \( \frac{-2\pi}{5}=-\frac{2}{5}\pi \).

Answer:

\(-\frac{2}{5}\) (the sign is \(-\), and the fraction is \(\frac{2}{5}\))