Trigonometric Identities and Relationships

Trigonometric Identities and Relationships

• Basic Trigonometric Functions:

  • Sine: $ext{sin}(x)$
  • Cosine: $ext{cos}(x)$

• Key Identities:

  • $ext{sin}^2(x) + ext{cos}^2(x) = 1$
  • $ext{sin}(x + y) = ext{sin}(x) ext{cos}(y) + ext{cos}(x) ext{sin}(y)$
  • $ext{cos}(x + y) = ext{cos}(x) ext{cos}(y) - ext{sin}(x) ext{sin}(y)$

• Combinations of Functions:

  • $ext{sin}(x) ext{cos}(y)$
  • $ext{cos}(x) ext{sin}(y)$

• Sine and Cosine Differences:

  • $1 - ext{sin}^3(x)$
  • $1 - ext{sin}(x)$

• Additional Combinations:

  • General forms and variations involving sine and cosine functions.