Trigonometric Functions Quiz

Trigonometric Functions

Cotangent (cot)

• Definition: The reciprocal of the tangent function
• Formula: cot(θ) = 1 / tan(θ) = cos(θ) / sin(θ)
• Range: (-∞, ∞)
• Properties:
  • cot(0) = undefined
  • cot(π/2) = 0
  • cot(-θ) = -cot(θ)

Sine (sin)

• Definition: The ratio of the opposite side to the hypotenuse in a right-angled triangle
• Formula: sin(θ) = opposite side / hypotenuse
• Range: [-1, 1]
• Properties:
  • sin(0) = 0
  • sin(π/2) = 1
  • sin(-θ) = -sin(θ)

Cosine (cos)

• Definition: The ratio of the adjacent side to the hypotenuse in a right-angled triangle
• Formula: cos(θ) = adjacent side / hypotenuse
• Range: [-1, 1]
• Properties:
  • cos(0) = 1
  • cos(π/2) = 0
  • cos(-θ) = cos(θ)

Tangent (tan)

• Definition: The ratio of the sine to the cosine
• Formula: tan(θ) = sin(θ) / cos(θ)
• Range: (-∞, ∞)
• Properties:
  • tan(0) = 0
  • tan(π/2) = undefined
  • tan(-θ) = -tan(θ)

Cosecant (csc)

• Definition: The reciprocal of the sine function
• Formula: csc(θ) = 1 / sin(θ)
• Range: (-∞, -1] ∪ [1, ∞)
• Properties:
  • csc(0) = undefined
  • csc(π/2) = 1
  • csc(-θ) = -csc(θ)

Secant (sec)

• Definition: The reciprocal of the cosine function
• Formula: sec(θ) = 1 / cos(θ)
• Range: (-∞, -1] ∪ [1, ∞)
• Properties:
  • sec(0) = 1
  • sec(π/2) = undefined
  • sec(-θ) = sec(θ)