Problem 90 - Algebra and Trigonometry

Question

What is the amplitude of the sine function? What does this tell you about the graph?

Step-by-Step Solution

Answer

The amplitude of the sine function is the absolute value of the coefficient of sine in the function, reflecting the function's maximum value. The amplitude affects the graph by changing its vertical stretch or compression. For the standard sine function, \( y = \sin(x) \), the amplitude is 1.

Step 1: Define Amplitude of sine function

The amplitude of sine function is the distance from the peak (or the bottom) of the graph to the resting position, which is generally the middle of the graph. Specifically for the function \( y = a \sin(bx + c) + d \), the amplitude is the absolute value of \( a \).

Step 2: Describe the amplitude of sine function

The amplitude of the standard sine function \( y = \sin(x) \) is 1. This is because the sine function's output ranges from -1 to 1, thus the maximum distance from the peak to the resting position is 1.

Step 3: Interpretation of the amplitude of sine function on the graph

The amplitude of the sine function determines the vertical stretch or compression of the function. A larger amplitude means a greater vertical stretch (the graph looks taller), and a smaller amplitude means a greater vertical compression (the graph looks flatter).