Trigonometry Short Course Tutorial by Lauren Johnson

Introduction

• Trigonometry focuses on relationships of sides and angles in triangles.
• Derived from Greek words 'trigonon' (triangle) and 'metron' (measure).
• Important in Geometry, Algebra, and Calculus.

Understand How Angles Are Measured

• Degrees:
  • Circle has 360 degrees (one revolution).
  • Primarily describes angle size.
• Radians:
  • One revolution equals 2π radians.
  • Conversion: 360° = 2π radians, 1° = π/180 radians.
  • Example conversions provided (e.g., 60° = π/3 radians).
• Unit Circle:
  • Centered at the origin, radius = 1.
  • Equation: x² + y² = 1.

Trigonometric Functions

• Six main ratios: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), cotangent (cot).
• SOH-CAH-TOA mnemonic:
  • Sine = Opposite/Hypotenuse
  • Cosine = Adjacent/Hypotenuse
  • Tangent = Opposite/Adjacent
• Reciprocal functions:
  • csc = 1/sin, sec = 1/cos, cot = 1/tan
• Practice examples using these identities.

Finding Trigonometric Values

• Given Angle Measure:
  • Use unit circle or special triangles (30°, 45°, 60°).
  • Calculators can find values for any angle.
• Missing Side Lengths:
  • Use given angle and known side with trig functions to solve.
• Finding Angle Measures:
  • Use inverse trig functions on calculator.

Using Definitions and Identities of Trig Functions

• Fundamental Identities:
  • Reciprocal, Quotient, and Pythagorean Identities.
• Sum and Difference Formulas:
  • For sin and cos: e.g., sin(A ± B) = sinA cosB ± cosA sinB
• Double and Half Angle Formulas:
  • For example, sin(2θ) = 2sinθ cosθ.
• Practice finding exact values using identities.

Key Features of Graphs of Trig Functions

• Sine and Cosine Functions:
  • Periodic with period 2π.
  • Amplitude and phase shift affect graph's shape and position.
• Tangent Function:
  • Period π, no amplitude (extends to ±∞).
  • Vertical asymptotes where cos(x) = 0.
• Use of technology (TI Calculator, Desmos) to graph functions.

Practice Problems

• Various exercises provided to reinforce learning.

Solutions

• Solutions to practice problems for self-assessment.

Note: Additional resources include Khan Academy videos for further clarification on each topic.