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.