Questions: Find an equation for the graph. Type the equation of the given graph in the form y=A sin Bx or y=A cos Bx. (Type an equation. Use integers or fractions for any numbers in the equation. Simplify your answer.)

$Find an equation for the graph. Type the equation of the given graph in the form y=A sin Bx or y=A cos Bx. (Type an equation. Use integers or fractions for any numbers in the equation. Simplify your answer.)$

Transcript text: Find an equation for the graph. Type the equation of the given graph in the form $y=A \boldsymbol{\operatorname { s i n }} B x$ or $y=A \cos B x$. (Type an equation. Use integers or fractions for any numbers in the equation. Simplify your answer.)

Solution

Solution Steps

Step 1: Find the amplitude

The amplitude (A) is the distance from the midline to the maximum or minimum value of the function. In this graph, the midline is y=0, and the maximum value is 2. Thus, the amplitude is 2.

Step 2: Determine the period

The period is the length of one complete cycle of the function. Here, one full cycle completes from x= -π/2 to x = π/2. Therefore, the period is π/2 - (-π/2) = π.

Step 3: Calculate B

The period is related to B by the equation Period = 2π/B. We found the period to be π, so π = 2π/B. Solving for B gives B=2.

Step 4: Decide on sine or cosine

The graph resembles a cosine wave starting at its maximum point. We can therefore use the cosine function.