基本概念

繪圖順序:

取圓心: O = 圓心
取半徑畫出圓形: OR = OC = 半徑
以直角畫出以下交點: ∠OAC = ∠OBC = ∠OCD = 直角 = 90°

三角函數:
正弦 = sin θ = AC/OR = OB/OR = sine
餘弦 = cos θ = BC/OR = OA/OR = cosine
正切 = tan θ = CD/OR = tangent
餘切 = cot θ = CE/OR = cotangent
正割 = sec θ = OD/OR = secand
餘割 = csc θ = OE/OR = cosecant
Θ = ∠COA = ∠OCB = ∠ACD = ∠OED

另外可參考很棒的三角函數圖解

角度與弧度

弧度又稱為弳度, 可簡化數學表示式.
rad = deg x (π / 180°). = Radian.
deg = rad x (180° / π). = Degree = Angle.

常見弧度
1 = (180° / π) = 圓弧長度等於半徑時的圓心角, 約為 57.29577951°.
2π = 360°, 全圓.
π = 180°, 半圓.
π/2 = 90°, 直角.
π/3 = 60°.
π/4 = 45°.
π/6 = 30°.
π/180 = 1°.

常用公式

三角形標示
若三角形三邊長 = a, b, c, 則
∠a = ∠bac = 邊長 a 的對角.
∠b = ∠abc = 邊長 b 的對角.
∠c = ∠acb = 邊長 c 的對角.
∠a + ∠b + ∠c = 180°.

畢氏定理、勾股定理: (適用於直角三角形)
a^2 + b^2 = c^2

餘弦定理 (適用於所有三角形)
(a^2 + b^2 - 2ab) x cos(c)) = c^2

        /// 將角度換算為弧度. 
        public static double GetRadian(double dDegree)
        {
            return dDegree * Math.PI / 180.0;
        }

        /// 將弧度換算為角度. 
        public static double GetDegree(double dRadians)
        {
            return dRadians * 180.0 / Math.PI;
        }

        /// 直角三角形已知(臨邊長度x)與(對邊長度y), 求斜邊(半徑 Radius)長度.
        public static double GetTriRadius(Point p1)
        {
            return GetTriRadius(p1.X, p1.Y);
        }

        /// 直角三角形已知(臨邊長度x)與(對邊長度y), 求斜邊(半徑 Radius)長度.
        public static double GetTriRadius(double x, double y)
        {
            return Math.Sqrt(x * x + y * y); // CodeHelper.
        }

        /// 取得 點 的角度.
        public static double GetTriDegree(Point p1)
        {
            return GetTriDegree(p1.X, p1.Y);
        }

        /// 取得 點(y, x) 的角度.
        public static double GetTriDegree(double x, double y)
        {
            return GetDegree(Math.Atan2(y, x)); // CodeHelper. 
        }

        /// 直角三角形已知斜邊(半徑)長度及角度, 求(臨邊長度x).
        public static double GetTriX(double dDegree, double dRadius)
        {
            return dRadius * Math.Cos(GetRadian(dDegree));
        }

        /// 直角三角形已知斜邊(半徑)長度及角度, 求(對邊長度y).
        public static double GetTriY(double dDegree, double dRadius)
        {
            return dRadius * Math.Sin(GetRadian(dDegree));
        }

        /// 直角三角形已知斜邊(半徑)長度及角度, 求(臨邊長度x)及(對邊長度y).
        public static Point GetTriPoint(double dDegree, double dRadius)
        {
            return new Point(
                GetTriX(dDegree, dRadius),
                GetTriY(dDegree, dRadius));
        }

        /// 已知三邊長, 取得三角形3個角角度.
        public static void GetTriangleDegrees(double a, double b, double c, out double bac, out double abc, out double acb)
        {
            double CosA = (Math.Pow(b, 2.0) + Math.Pow(c, 2.0) - Math.Pow(a, 2.0)) / (2.0 * b * c);
            double CosB = (Math.Pow(a, 2.0) + Math.Pow(c, 2.0) - Math.Pow(b, 2.0)) / (2.0 * c * a);
            double CosC = (Math.Pow(a, 2.0) + Math.Pow(b, 2.0) - Math.Pow(c, 2.0)) / (2.0 * a * b);
            bac = GetDegree(Math.Acos(CosA));
            abc = GetDegree(Math.Acos(CosB));
            acb = GetDegree(Math.Acos(CosC));
        }

常用角度

中英對照

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