key term - Degree

Definition

In the context of mathematics, the term 'degree' refers to the measure of a specific angle or the highest exponent of a polynomial function. It is a fundamental concept that is essential in understanding various mathematical topics, including power functions, polynomial functions, trigonometry, and the solving of trigonometric equations.

5 Must Know Facts For Your Next Test

1. The degree of a power function is the exponent of the variable in the function.
2. The degree of a polynomial function is the highest exponent of the variable in the function.
3. The degree of an angle is a measure of the rotation of a line or plane, with a full circle (360°) representing 360 degrees.
4. The unit circle in trigonometry is used to define the sine and cosine functions, which are periodic functions with a period of 360 degrees.
5. Solving trigonometric equations often involves finding the angles that satisfy the equation, which are typically expressed in degrees or radians.

Review Questions

• Explain how the degree of a power function relates to the exponent of the variable in the function.
  • The degree of a power function is directly related to the exponent of the variable in the function. Specifically, the degree of a power function $f(x) = x^n$ is equal to the exponent $n$. This means that the degree of the function represents the power to which the variable $x$ is raised, which determines the shape and behavior of the function's graph.
• Describe how the degree of a polynomial function is determined and how it affects the graph of the function.
  • The degree of a polynomial function is the highest exponent of the variable in the function. For example, in the polynomial function $f(x) = 3x^4 - 2x^2 + 5$, the degree of the function is 4, as the highest exponent of the variable $x$ is 4. The degree of a polynomial function directly influences the shape of its graph, with higher-degree polynomials having more complex and varied shapes compared to lower-degree polynomials.
• Explain the significance of the degree of an angle in the context of the unit circle and trigonometric functions, and how it relates to solving trigonometric equations.
  • In the unit circle, the degree of an angle represents the measure of the rotation of a line or plane, with a full circle (360°) representing 360 degrees. This degree measure is crucial in defining the sine and cosine functions, which are periodic functions with a period of 360 degrees. When solving trigonometric equations, the solutions are often expressed in terms of the degree measure of the angles that satisfy the equation. Understanding the degree of an angle and its relationship to the unit circle and trigonometric functions is essential for effectively solving trigonometric equations.

Related terms

Angle: A measure of the rotation between two intersecting lines or planes, typically expressed in degrees or radians.

Exponent:

The power to which a base number is raised, indicating the number of times the base is multiplied by itself.

Polynomial Function:

A function that is the sum of one or more terms, each of which is the product of a constant and one or more variables raised to a non-negative integer power.