Trigonometric functions
12 Questions
3 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

Which property of algebraic equations states that the order of variables and constants does not change the equation?

  • Associative Property
  • Transitive Property
  • Commutative Property (correct)
  • Distributive Property

    • What is the degree of the variable in a linear equation?

  • 2
  • _can be any whole number
  • 1 (correct)
  • 3

    • What is the method used to solve quadratic equations of the form ax^2 + bx + c = 0?

  • Multiplication and Division
  • Quadratic Formula (correct)
  • Addition and Subtraction
  • Factoring

    • What type of equation has a degree of the variable(s) of 3 or higher?

    <p>Polynomial Equation</p> Signup and view all the answers

    Which of the following is an application of algebraic equations?

    <p>Modeling real-world problems</p> Signup and view all the answers

    What is the purpose of the Distributive Property in solving algebraic equations?

    <p>To combine like terms</p> Signup and view all the answers

    What is the ratio of the opposite side to the hypotenuse in a right-angled triangle?

    <p>Sine</p> Signup and view all the answers

    What is the Pythagorean Identity in trigonometry?

    <p>sin²(x) + cos²(x) = 1</p> Signup and view all the answers

    Which of the following formulas is used to find the sine of the sum of two angles?

    <p>sin(a + b) = sin(a)cos(b) + cos(a)sin(b)</p> Signup and view all the answers

    What is the period of a trigonometric function?

    <p>360°</p> Signup and view all the answers

    What is the application of trigonometry in finding unknown sides and angles in triangles?

    <p>Triangulation</p> Signup and view all the answers

    What is the double angle formula for cosine?

    <p>cos(2x) = cos²(x) - sin²(x)</p> Signup and view all the answers

    Study Notes

    Algebraic Equations

    Definition

    • An algebraic equation is an equation involving variables and constants, where the variables are raised to a power (usually a whole number) and combined using addition, subtraction, multiplication, and division.

    Types of Algebraic Equations

    • Linear Equations: degree of the variable(s) is 1
      • Example: 2x + 3 = 5
    • Quadratic Equations: degree of the variable(s) is 2
      • Example: x^2 + 4x + 4 = 0
    • Polynomial Equations: degree of the variable(s) is 3 or higher
      • Example: x^3 - 2x^2 + x - 1 = 0

    Properties of Algebraic Equations

    • Commutative Property: the order of variables and constants does not change the equation
    • Associative Property: the order in which operations are performed does not change the equation
    • Distributive Property: multiplication distributes over addition

    Solving Algebraic Equations

    • Addition and Subtraction: add or subtract the same value to both sides of the equation
    • Multiplication and Division: multiply or divide both sides of the equation by the same non-zero value
    • Factoring: express the equation as a product of simpler equations
    • Quadratic Formula: used to solve quadratic equations of the form ax^2 + bx + c = 0

    Applications of Algebraic Equations

    • Modeling Real-World Problems: algebraic equations can be used to model population growth, electrical circuits, and other real-world phenomena
    • Science and Engineering: algebraic equations are used to describe the laws of physics, chemistry, and other scientific fields

    Algebraic Equations

    Definition

    • Involves variables and constants combined using addition, subtraction, multiplication, and division
    • Variables are raised to a power (usually a whole number)

    Types of Algebraic Equations

    Linear Equations

    • Degree of the variable(s) is 1
    • Example: 2x + 3 = 5

    Quadratic Equations

    • Degree of the variable(s) is 2
    • Example: x^2 + 4x + 4 = 0

    Polynomial Equations

    • Degree of the variable(s) is 3 or higher
    • Example: x^3 - 2x^2 + x - 1 = 0

    Properties of Algebraic Equations

    Commutative Property

    • Order of variables and constants does not change the equation

    Associative Property

    • Order in which operations are performed does not change the equation

    Distributive Property

    • Multiplication distributes over addition

    Solving Algebraic Equations

    Elementary Operations

    • Add or subtract the same value to both sides of the equation
    • Multiply or divide both sides of the equation by the same non-zero value

    Factoring

    • Express the equation as a product of simpler equations

    Quadratic Formula

    • Used to solve quadratic equations of the form ax^2 + bx + c = 0

    Applications of Algebraic Equations

    Modeling Real-World Problems

    • Algebraic equations can be used to model population growth, electrical circuits, and other real-world phenomena

    Science and Engineering

    • Algebraic equations are used to describe the laws of physics, chemistry, and other scientific fields

    Trigonometric Functions

    Definition and Basics

    • Trigonometric functions are based on the ratios of sides in right-angled triangles.
    • There are three basic trigonometric functions: sine (sin), cosine (cos), and tangent (tan), which are defined as:
      • Sine (sin): opposite side / hypotenuse
      • Cosine (cos): adjacent side / hypotenuse
      • Tangent (tan): opposite side / adjacent side

    Identities and Formulas

    • The Pythagorean Identity states that sin²(x) + cos²(x) = 1.
    • The Sum and Difference Formulas are:
      • sin(a + b) = sin(a)cos(b) + cos(a)sin(b)
      • cos(a + b) = cos(a)cos(b) - sin(a)sin(b)
      • tan(a + b) = (tan(a) + tan(b)) / (1 - tan(a)tan(b))
    • The Double Angle Formulas are:
      • sin(2x) = 2sin(x)cos(x)
      • cos(2x) = cos²(x) - sin²(x)
      • tan(2x) = (2tan(x)) / (1 - tan²(x))

    Graphs and Properties

    • Trigonometric functions have a periodic nature, repeating every 360° (or 2π radians).
    • The amplitude is the maximum value of a trigonometric function.
    • A phase shift occurs when a trigonometric function is horizontally shifted.

    Applications

    • Triangulation is used to find unknown sides and angles in triangles.
    • Trigonometric functions model real-world phenomena, such as sound waves, light waves, and electrical signals.
    • Analytic geometry uses trigonometry to define curves and surfaces.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    Description

    L

    More Like This

    Use Quizgecko on...
    Browser
    Open
    Browser
    Browser