what is the amplitude of the following function? y = \\frac{3}{2} \\sin(x + 4)

Explanation:

Step1: Recall the amplitude formula

For a sine function in the form ( y = A\sin(Bx + C) + D ), the amplitude is given by ( |A| ).

Step2: Identify the value of ( A ) in the given function

In the function ( y=\frac{3}{2}\sin(x + 4) ), we can see that ( A=\frac{3}{2} ).

Step3: Calculate the amplitude

Using the formula for amplitude, we take the absolute value of ( A ). Since ( A = \frac{3}{2} ) and ( \left|\frac{3}{2}\right|=\frac{3}{2} ), the amplitude is ( \frac{3}{2} ).

Answer:

(\frac{3}{2})