(26) Evaluating Inverse Trigonometric Functions

Evaluating Inverse Sine Functions

• Arc Sine of 1/2:

  • Sine values: Sine(π/6) = 1/2 (valid)

  • Sine(5π/6) = 1/2 (invalid).

  • Answer: Arc sine(1/2) = π/6.

• Understanding Quadrants:

  • Arc sine exists in Quadrant I (0 to π/2) and Quadrant IV (-π/2 to 0).

• Arc Sine of √3/2:

  • Sine(π/3) = √3/2 (valid)

  • Sine(120 degrees) = √3/2 (invalid).

  • Answer: Arc sine(√3/2) = π/3.

• Arc Sine of -1/2:

  • Valid: Sine(-30 degrees) = -1/2.

  • Answer: Arc sine(-1/2) = -π/6.

• Arc Sine of -√2/2:

  • Valid: Sine(-45 degrees) = -√2/2.

  • Answer: Arc sine(-√2/2) = -π/4.

• Special Values:

  • Arc sine(0) = 0, Arc sine(1) = π/2, Arc sine(-1) = -π/2.

Evaluating Inverse Cosine Functions

• Arc Cosine of 1/2:

  • Sine(π/3) = 1/2 (valid).

  • Answer: Arc cosine(1/2) = π/3.

• Arc Cosine of -√3/2:

  • Valid: Cosine(150 degrees) = -√3/2.

  • Answer: Arc cosine(-√3/2) = 5π/6.

• Arc Cosine of -√2/2:

  • Valid: Cosine(135 degrees) = -√2/2.

  • Answer: Arc cosine(-√2/2) = 3π/4.

• Special Values:

  • Arc cosine(0) = π/2, Arc cosine(1) = 0, Arc cosine(-1) = π.