正弦比
几何画板及绘图内容加载中,请稍等……
本范例演示正弦比的概念。通过构造三角形中的角度和边长,学生可以直观理解正弦比的定义及其在三角形中的应用。使用了Element, Point, Polygon, LaTeX, UnicodeToLetter, Angle, Join, TableText, Length等GeoGebra命令。适合初中及以上学生学习三角函数。
GeoGebra 命令及参数
Element(RatioLst, caseIndx) → currRatioPoint(Segment[(1, 0), (26, 0)]) → BPoint(Segment[(x(B), 0), (x(B), 13)]) → CPolygon(C, A, B) → t1, b, c, aLaTeX(If[isCorrect ∧ a ≠ 3, "=\dfrac{4}{5}", ""]) → correctCosLaTeX(If[isCorrect ∧ a ≠ 3, "=\dfrac{3}{5}", ""]) → correctSinLaTeX(If[IsInteger[lenHyp], (("" * lenHyp) * ""), (("\sqrt{" * bSq) * "}")]) → hypTxtUnicodeToLetter(10007) → xmarkUnicodeToLetter(10003) → cmarkAngle(C, B, A) → αPolygon(A, B, C) → t2, c_1, a_1, b_1LaTeX("A") → lblALaTeX("C") → lblCLaTeX("B") → lblBJoin({titleLst, Zip[{x(A), y(A)}, A, triList]}) → fullListTableText(fullList, "|111_111111111111l") → triTableAngle(B, A, C) → θLaTeX("\dfrac{3}{5}") → A4Length(RatioLst) → numCasesElement(RatioFormatedLst, caseIndx) → currRatioDispLaTeX((("\text{\textbf{Question: }How many right-triangles can you construct with \sin(\theta ) = \frac{opp}{hyp}=" * currRatioDisp) * " ?\\What is the value of \cos(\theta ) = \frac{adj}{hyp} for these triangles?} ")) → MainInstrucLaTeX("\dfrac{5}{13}") → C4LaTeX("\dfrac{4}{5}") → B4LaTeX("\text{\textbf{Instructions: }Drag vertex \(C\) up and down to change the height of the triangle, and slide \\vertex \(B\) left and right to change the width of the triangle.}") → SpecInstrucTableText({ratioData}, "v") → RatioTable
AI 绘图提示语参考
绘制一个直角三角形示意图,用于直观展示正弦比的概念。三角形底边水平放置,一个顶点位于底边上可左右滑动以改变宽度,另一个顶点在垂直方向可上下拖动以调整高度。图形中需标注角度θ和α,并以分数形式显示正弦比sin(θ)=对边/斜边的值(如3/5)和余弦比cos(θ)=邻边/斜边的值。包含一个数据表格,列出不同三角形配置下的比值信息。添加文本指令,指导用户通过拖动顶点来探索正弦比固定的直角三角形,并引导计算对应的余弦比值。
以上提示语为根据原始绘图命令整理而来,仅供参考。