Question

find the amplitude (a) and the period (p) of the following function.

\\y = 3 \cos(3x)\\

\\a = 3, p = \frac{?}{\square}\pi\\

Explanation:

⚡ Using what you learned: Amplitude, Period, Phase Shift

Step 1: Identify the general form

For a trigonometric function of the form \( y = a \cos(bx) \):

• Amplitude \( A = |a| \)
• Period \( P = \frac{2\pi}{|b|} \)

Given:

$$ y = 3 \cos(3x) $$

Here, \( a = 3 \) and \( b = 3 \).

Step 2: Calculate Amplitude and Period

• Amplitude:

$$ A = |3| = 3 $$

• Period:

$$ P = \frac{2\pi}{3} = \frac{2}{3}\pi $$

Answer:

The missing value in the numerator is 2 (making the period \( P = \frac{2}{3}\pi \)).