Question

question 22
$y = -2\cos(4x + \pi) - 1$, what is the period of this function?
(a) 2 \quad (b) $-\frac{\pi}{4}$ \quad (c) $\frac{\pi}{2}$ \quad (d) -2 \quad (e) $\frac{\pi}{4}$ \quad (f) $-\frac{\pi}{2}$
\bigcirc a
\bigcirc b
\bigcirc c
\bigcirc d
\bigcirc e
\bigcirc f

Explanation:

First Question (Amplitude)

Step1: Recall Amplitude Formula

For a cosine function \( y = A\cos(Bx + C) + D \), the amplitude is \( |A| \).

Step2: Identify \( A \) in Given Function

In \( y = -2\cos(4x + \pi) - 1 \), \( A = -2 \).

Step3: Calculate Amplitude

Amplitude \( = | -2 | = 2 \).

Step1: Recall Period Formula

For a cosine function \( y = A\cos(Bx + C) + D \), the period is \( \frac{2\pi}{|B|} \).

Step2: Identify \( B \) in Given Function

In \( y = -2\cos(4x + \pi) - 1 \), \( B = 4 \).

Step3: Calculate Period

Period \( = \frac{2\pi}{|4|} = \frac{2\pi}{4} = \frac{\pi}{2} \).

Answer:

a. 2

Second Question (Period)