{
  "unit": 10,
  "title": "Trigonometric Functions & Periodic Models",
  "terms": [
    {
      "en": "angle",
      "es": "ángulo",
      "fr": "angle",
      "ar": "زاوية",
      "pt": "ângulo",
      "definition": "Two rays sharing a vertex, measured in degrees or radians."
    },
    {
      "en": "radian",
      "es": "radián",
      "fr": "radian",
      "ar": "راديان",
      "pt": "radiano",
      "definition": "Angle subtending an arc equal in length to the circle radius."
    },
    {
      "en": "degree",
      "es": "grado",
      "fr": "degré",
      "ar": "درجة زاوية",
      "pt": "grau",
      "definition": "An angular unit equal to one 360th of a complete turn."
    },
    {
      "en": "unit circle",
      "es": "circunferencia unitaria",
      "fr": "cercle trigonométrique",
      "ar": "دائرة الوحدة",
      "pt": "círculo trigonométrico",
      "definition": "A circle with radius 1 centered at the origin."
    },
    {
      "en": "reference angle",
      "es": "ángulo de referencia",
      "fr": "angle de référence",
      "ar": "زاوية مرجعية",
      "pt": "ângulo de referência",
      "definition": "The acute angle between a terminal side and the x-axis."
    },
    {
      "en": "exact trig value",
      "es": "valor trigonométrico exacto",
      "fr": "valeur trigonométrique exacte",
      "ar": "قيمة مثلثية دقيقة",
      "pt": "valor trigonométrico exato",
      "definition": "An exact ratio or radical rather than a rounded decimal."
    },
    {
      "en": "sine function",
      "es": "función seno",
      "fr": "fonction sinus",
      "ar": "دالة الجيب",
      "pt": "função seno",
      "definition": "The y-coordinate of the unit-circle point at angle θ."
    },
    {
      "en": "cosine function",
      "es": "función coseno",
      "fr": "fonction cosinus",
      "ar": "دالة جيب التمام",
      "pt": "função cosseno",
      "definition": "The x-coordinate of the unit-circle point at angle θ."
    },
    {
      "en": "tangent function",
      "es": "función tangente",
      "fr": "fonction tangente",
      "ar": "دالة الظل",
      "pt": "função tangente",
      "definition": "sin(θ)/cos(θ), where cos(θ) is nonzero."
    },
    {
      "en": "reciprocal trig function",
      "es": "función trigonométrica recíproca",
      "fr": "fonction trigonométrique réciproque",
      "ar": "دالة مثلثية مقلوبة",
      "pt": "função trigonométrica recíproca",
      "definition": "A function such as secant, cosecant, or cotangent formed from reciprocal ratios."
    },
    {
      "en": "trig graph",
      "es": "gráfica trigonométrica",
      "fr": "graphe trigonométrique",
      "ar": "منحنى دالة مثلثية",
      "pt": "gráfico trigonométrico",
      "definition": "A plot of a trigonometric output against its angle input."
    },
    {
      "en": "sinusoidal model",
      "es": "modelo sinusoidal",
      "fr": "modèle sinusoïdal",
      "ar": "نموذج جيبي",
      "pt": "modelo senoidal",
      "definition": "A model y=A sin(B(x-C))+D or its cosine equivalent."
    },
    {
      "en": "midline",
      "es": "línea media",
      "fr": "droite médiane",
      "ar": "خط المنتصف",
      "pt": "linha média",
      "definition": "The horizontal line halfway between a sinusoid's maximum and minimum."
    },
    {
      "en": "amplitude",
      "es": "amplitud",
      "fr": "amplitude",
      "ar": "سعة الموجة",
      "pt": "amplitude",
      "definition": "Half a sinusoid's peak-to-trough distance."
    },
    {
      "en": "period",
      "es": "período",
      "fr": "période",
      "ar": "الدورة",
      "pt": "período",
      "definition": "The smallest positive horizontal interval after which a periodic function repeats."
    },
    {
      "en": "phase shift",
      "es": "desfase",
      "fr": "déphasage",
      "ar": "إزاحة الطور",
      "pt": "deslocamento de fase",
      "definition": "The horizontal displacement of a periodic graph relative to its reference."
    },
    {
      "en": "vertical shift",
      "es": "desplazamiento vertical",
      "fr": "décalage vertical",
      "ar": "إزاحة رأسية",
      "pt": "deslocamento vertical",
      "definition": "Adding a constant to all output values."
    },
    {
      "en": "cotangent",
      "es": "cotangente",
      "fr": "cotangente",
      "ar": "ظل التمام",
      "pt": "cotangente",
      "definition": "cos(θ)/sin(θ), defined when sin(θ) is nonzero."
    },
    {
      "en": "secant",
      "es": "secante",
      "fr": "sécante",
      "ar": "القاطع",
      "pt": "secante",
      "definition": "1/cos(θ), defined when cosine is nonzero."
    },
    {
      "en": "inverse trigonometric function",
      "es": "función trigonométrica inversa",
      "fr": "fonction trigonométrique réciproque au sens inverse",
      "ar": "دالة مثلثية عكسية",
      "pt": "função trigonométrica inversa",
      "definition": "A principal-angle function such as arcsin that reverses sine on a restricted domain."
    },
    {
      "en": "trigonometric regression",
      "es": "regresión trigonométrica",
      "fr": "régression trigonométrique",
      "ar": "الانحدار المثلثي",
      "pt": "regressão trigonométrica",
      "definition": "Fitting a periodic sine or cosine model to observations."
    },
    {
      "en": "periodic data",
      "es": "datos periódicos",
      "fr": "données périodiques",
      "ar": "بيانات دورية",
      "pt": "dados periódicos",
      "definition": "Measurements that repeat a pattern at regular intervals."
    },
    {
      "en": "vector",
      "es": "vector",
      "fr": "vecteur",
      "ar": "متجه",
      "pt": "vetor",
      "definition": "A quantity with magnitude and direction."
    },
    {
      "en": "vector magnitude",
      "es": "magnitud vectorial",
      "fr": "norme vectorielle",
      "ar": "مقدار المتجه",
      "pt": "módulo do vetor",
      "definition": "The length of a vector, sqrt(x²+y²) in two dimensions."
    },
    {
      "en": "bearing",
      "es": "rumbo",
      "fr": "relèvement",
      "ar": "اتجاه ملاحي",
      "pt": "rumo",
      "definition": "A compass-referenced angle describing direction."
    },
    {
      "en": "vector component",
      "es": "componente vectorial",
      "fr": "composante vectorielle",
      "ar": "مركبة المتجه",
      "pt": "componente vetorial",
      "definition": "The projection of a vector along a coordinate axis."
    }
  ],
  "schema_version": "1.1"
}