Trigonometry: Angles, Identities, and Graphs

Trigonometry

Key Concepts

• Angles and Triangles:
  • Sine (sin), Cosine (cos), and Tangent (tan) ratios
  • Pythagorean Identity: sin^2(A) + cos^2(A) = 1
• Trigonometric Identities:
  • Sum and Difference Formulas
  • Double and Half Angle Formulas
• Graphs of Trigonometric Functions:
  • Sine, Cosine, and Tangent curves
  • Amplitude, Period, and Phase Shift

Important Formulas

• 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))

Algebra

Key Concepts

• Equations and Inequalities:
  • Linear and Quadratic Equations
  • Systems of Equations
  • Inequality notation and solutions
• Functions:
  • Domain and Range
  • Composition and Inverse Functions
• Graphing:
  • Linear and Quadratic Functions
  • Intercepts, Vertex, and Axis of Symmetry

Important Formulas

• Quadratic Formula: x = (-b ± √(b^2 - 4ac)) / 2a
• Vertex Form: f(x) = a(x - h)^2 + k

Statistics

Key Concepts

• Descriptive Statistics:
  • Measures of Central Tendency (Mean, Median, Mode)
  • Measures of Variability (Range, Variance, Standard Deviation)
• Data Visualization:
  • Histograms, Box Plots, and Scatter Plots
• Probability:
  • Basic Concepts (Experiment, Outcome, Event)
  • Rules of Probability (Addition, Multiplication, Conditional)

Important Formulas

• Mean: μ = (Σx) / n
• Variance: σ^2 = (Σ(x - μ)^2) / n
• Standard Deviation: σ = √(σ^2)

Trigonometry

Angles and Triangles

• Sine (sin), Cosine (cos), and Tangent (tan) are ratios of the lengths of the sides of a right triangle.
• The Pythagorean Identity states that sin^2(A) + cos^2(A) = 1, where A is an angle.

Trigonometric Identities

• Sum and Difference Formulas are used to find the sine, cosine, and tangent of the sum or difference of two angles.
• Double and Half Angle Formulas are used to find the sine, cosine, and tangent of double or half an angle.

Graphs of Trigonometric Functions

• Sine, Cosine, and Tangent curves have amplitude, period, and phase shift.
• Amplitude is the maximum value of the function, period is the time it takes to complete one cycle, and phase shift is the horizontal shift of the function.

Important Formulas

• sin(A + B) = sin(A)cos(B) + cos(A)sin(B) is the sum formula for sine.
• cos(A + B) = cos(A)cos(B) - sin(A)sin(B) is the sum formula for cosine.
• tan(A + B) = (tan(A) + tan(B)) / (1 - tan(A)tan(B)) is the sum formula for tangent.

Algebra

Equations and Inequalities

• Linear and Quadratic Equations can be solved using various methods, such as factoring and the quadratic formula.
• Systems of Equations can be solved using substitution, elimination, or graphing.
• Inequality notation and solutions are used to represent and solve inequalities.

Functions

• Domain and Range are the sets of input and output values of a function.
• Composition and Inverse Functions are used to combine and reverse functions.

Graphing

• Linear and Quadratic Functions can be graphed using various methods, such as table of values and intercepts.
• Intercepts, Vertex, and Axis of Symmetry are key features of quadratic functions.

Important Formulas

• The Quadratic Formula x = (-b ± √(b^2 - 4ac)) / 2a is used to solve quadratic equations.
• Vertex Form f(x) = a(x - h)^2 + k is a standard form of quadratic functions.

Statistics

Descriptive Statistics

• Measures of Central Tendency (Mean, Median, Mode) are used to describe the center of a dataset.
• Measures of Variability (Range, Variance, Standard Deviation) are used to describe the spread of a dataset.

Data Visualization

• Histograms, Box Plots, and Scatter Plots are used to visualize and understand data.

Probability

• Basic Concepts (Experiment, Outcome, Event) are used to describe probability.
• Rules of Probability (Addition, Multiplication, Conditional) are used to calculate probabilities.

Important Formulas

• The Mean μ = (Σx) / n is the average value of a dataset.
• The Variance σ^2 = (Σ(x - μ)^2) / n is a measure of the spread of a dataset.
• The Standard Deviation σ = √(σ^2) is a measure of the spread of a dataset.