Further Trig

Further Trig

Understanding Compound and Double Angle Formulas

• The compound angle formulas:
  • sin(A ± B) = sinA cosB ± cosA sinB
  • cos(A ± B) = cosA cosB ∓ sinA sinB
  • tan(A ± B) = (tanA ± tanB) / (1 ∓ tanA tanB)
• The double angle formulas:
  • sin2A = 2sinA cosA
  • cos2A = cos²A – sin²A = 2cos²A – 1 = 1 – 2sin²A
  • tan2A = 2tanA / (1 – tan²A)

Understanding of Radians and Degrees

• The angles can be measured in either radians or degrees.
• Conversion between them is essential:
  • 1 radian = 180/π degrees
  • 1 degree = π/180 radians

Creation and Manipulation of Trig Equations

• Trig equations can be manipulated and solved using trig identities.
• Common identities include:
  • sin²x + cos²x = 1
  • tanx = sinx/cosx
  • secx = 1/cosx
  • cosecx = 1/sinx

Grasping the Concepts of Trig Graphs

• Understanding the shape, period and amplitude of sine, cosine and tangent graphs is crucial.
• These graphs repeat after a certain interval, known as the Period. For sine and cosine, this is 2π (or 360°), while for tangent, it’s π (or 180°).

Advanced Concepts in Trigonometry

• Understanding the concept of inverse trigonometric functions, i.e., arcsin, arccos, and arctan.
• Familiarity with trigonometric equations and inequalities and how to solve them.
• Knowledge of trigonometric series, including the formulas for sine and cosine in terms of exponential functions.