Math / Trigonometry

QuestionDetermine the amplitude of the sinusoidal function $y=-3 \sin \left[2\left[x-\frac{\pi}{3}\right)\right]+1$ . a) b) -3 c) 2 d) $\frac{\pi}{3}$

Studdy Solution

STEP 1

1. The function given is a sinusoidal function of the form $y = A \sin(B(x - C)) + D$ .
2. The amplitude of a sinusoidal function $y = A \sin(Bx)$ or $y = A \cos(Bx)$ is given by the absolute value of the coefficient $A$ .

STEP 2

1. Identify the coefficient $A$ in the sinusoidal function.
2. Calculate the amplitude as the absolute value of $A$ .

STEP 3

Identify the coefficient $A$ in the function $y = -3 \sin \left[ 2 \left( x - \frac{\pi}{3} \right) \right] + 1$ .
In this function, the coefficient $A$ is the number in front of the sine function. Here, $A = -3$ .

STEP 4

Calculate the amplitude of the function. The amplitude is the absolute value of $A$ .
$\text{Amplitude} = |A| = |-3| = 3$
The amplitude of the sinusoidal function is $\boxed{3}$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms