{
  "sin": {
    "equation": "y = sin x",
    "domain": "(-∞, ∞)",
    "range": "[-1, 1]",
    "period": "2π",
    "keyPoints": [
      [0, 0],
      ["π/2", 1],
      ["π", 0],
      ["3π/2", -1],
      ["2π", 0]
    ],
    "shape": "Smooth wave starting from origin"
  },
  "cos": {
    "equation": "y = cos x",
    "domain": "(-∞, ∞)",
    "range": "[-1, 1]",
    "period": "2π",
    "keyPoints": [
      [0, 1],
      ["π/2", 0],
      ["π", -1],
      ["3π/2", 0],
      ["2π", 1]
    ],
    "shape": "Wave starting from maximum at y=1"
  },
  "tan": {
    "equation": "y = tan x",
    "domain": "x ≠ (2n+1)π/2",
    "range": "(-∞, ∞)",
    "period": "π",
    "asymptotes": ["x = ±π/2, ±3π/2, ..."],
    "keyPoints": [
      [0, 0],
      ["π/4", 1],
      ["-π/4", -1]
    ],
    "shape": "Increasing curve between asymptotes"
  },
  "cot": {
    "equation": "y = cot x",
    "domain": "x ≠ nπ",
    "range": "(-∞, ∞)",
    "period": "π",
    "asymptotes": ["x = 0, ±π, ±2π, ..."],
    "shape": "Decreasing curve between asymptotes"
  },
  "sec": {
    "equation": "y = sec x",
    "domain": "x ≠ (2n+1)π/2",
    "range": "(-∞, -1] ∪ [1, ∞)",
    "asymptotes": ["x = ±π/2, ±3π/2, ..."],
    "shape": "U-shaped branches"
  },
  "cosec": {
    "equation": "y = cosec x",
    "domain": "x ≠ nπ",
    "range": "(-∞, -1] ∪ [1, ∞)",
    "asymptotes": ["x = 0, ±π, ±2π, ..."],
    "shape": "U-shaped inverted branches"
  },
  "sin_inverse": {
    "equation": "y = sin⁻¹ x",
    "domain": "[-1, 1]",
    "range": "[-π/2, π/2]",
    "monotonic": "Increasing",
    "keyPoints": [
      [-1, "-π/2"],
      [0, 0],
      [1, "π/2"]
    ]
  },
  "cos_inverse": {
    "equation": "y = cos⁻¹ x",
    "domain": "[-1, 1]",
    "range": "[0, π]",
    "monotonic": "Decreasing",
    "keyPoints": [
      [-1, "π"],
      [0, "π/2"],
      [1, 0]
    ]
  },
  "tan_inverse": {
    "equation": "y = tan⁻¹ x",
    "domain": "(-∞, ∞)",
    "range": "(-π/2, π/2)",
    "asymptotes": ["y = ±π/2"],
    "shape": "S-shaped curve through origin"
  }
}