Question

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

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

\\a = ?, p = \frac{\box}{\box}\pi\\

Explanation:

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

Step 1: Identify the Amplitude

For a trigonometric function of the form \( y = a \cos(bx) \), the amplitude \( A \) is given by:

$$ A = |a| $$

Given the function \( y = 3 \cos(3x) \):

$$ a = 3 $$

$$ A = |3| = 3 $$

Step 2: Identify the Period

The period \( P \) of a cosine function is calculated using the formula:

$$ P = \frac{2\pi}{|b|} $$

Given the function \( y = 3 \cos(3x) \):

$$ b = 3 $$

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

Answer:

$$ A = 3, \quad P = \frac{2}{3}\pi $$