Q2. - Algebra 2

Question

Define the midline of the trigonometric graph.

Step-by-Step Solution

Answer

The mid line of a trigonometric graph is a new reference line when the parent graph is stretched vertically up or down and then the graph oscillates about new reference line which is called the midline of the trigonometric graph.

Step 1. Write down the given information.

The given statement is to define the concept of midline of trigonometric graph.

Step 2. Concept used.

A function of the form:

$y=a\sin b\left(\theta -h\right)+k,y=a\cos b\left(\theta -h\right)+k \text{and }y=a\tan b\left(\theta -h\right)+k$ has vertical shift $\left(k\right)$. And, a period of $\frac{360°}{\left|b\right|} \text{or }\frac{2\pi }{\left|b\right|}$ for sine, cosecant, secant and cosine functions and a period of $\frac{180°}{\left|b\right|} \text{or }\frac{\pi }{\left|b\right|}$ for tangent and cotangent function. The phase shift for the functions is $\left(h\right)$.

The amplitude of secant, cosecant, tangent and cotangent functions is not defined.

The equation for the midline is written as, $y=k$. A midline is a new reference line when the parent graph is stretched vertically up or down and then the graph oscillates about new reference line called the midline.

Step 3. Definition of midline for a trigonometric graph.

With the help of concept stated above, the mid line of a trigonometric graph is a new reference line when the parent graph is stretched vertically up or down and then the graph oscillates about new reference line which is called the midline of the trigonometric graph.