Question

what is the amplitude of the following function?
y = √3(1 + cos x)
√?

Explanation:

Step1: Recall Amplitude Formula

For a cosine function in the form \( y = A + B\cos(Cx + D) \), the amplitude is \( |B| \). First, expand the given function: \( y=\sqrt{3}+\sqrt{3}\cos x \).

Step2: Identify B Value

In the expanded form, the coefficient of \( \cos x \) (which is \( B \)) is \( \sqrt{3} \). The amplitude is the absolute value of \( B \), and since \( \sqrt{3} \) is positive, the amplitude is \( \sqrt{3} \). But we need to find the value inside the square root in the box. Let the amplitude be \( \sqrt{k} \), so \( \sqrt{k}=\sqrt{3} \), which means \( k = 3 \).

Answer:

3