特殊角的三角函数值记忆训练
2020-03-13 07:38
本GeoGebra范例旨在帮助学生进行特殊角三角函数值的记忆与测试训练。通过随机生成正弦和余弦的特殊角题目，结合表格文本与交互按钮，用户可自我检测对常见特殊角三角函数值的掌握程度。范例运用随机元素、序列及条件判断等命令，构建了动态数学练习环境，有效提升学习效率。
所属专题
中职数学GeoGebra互动教学资源库
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SetBackgroundColor(cosz4,"蓝绿")
SetBackgroundColor(cosz5,"蓝绿")
SetBackgroundColor(cosz6,"蓝绿")
SetBackgroundColor(cosz7,"蓝绿")
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SetBackgroundColor(cosz10,"蓝绿")
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SetBackgroundColor(cosz4,"蓝绿")
SetBackgroundColor(cosz5,"蓝绿")
SetBackgroundColor(cosz6,"蓝绿")
SetBackgroundColor(cosz7,"蓝绿")
SetBackgroundColor(cosz8,"蓝绿")
SetBackgroundColor(cosz9,"蓝绿")
SetBackgroundColor(cosz10,"蓝绿")
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<command name="LaTeX">
<input a0=""\frac{\sqrt3}{2}""/>
<output a0="cosz2"/>
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<element type="text" label="cosz2">
<show object="false" label="true" ev="8"/>
<condition showObject="hsmc ≟ "cos""/>
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SetBackgroundColor(cosz4,"蓝绿")
SetBackgroundColor(cosz5,"蓝绿")
SetBackgroundColor(cosz6,"蓝绿")
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SetBackgroundColor(cosz9,"蓝绿")
SetBackgroundColor(cosz10,"蓝绿")
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<command name="LaTeX">
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<condition showObject="hsmc ≟ "cos""/>
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<command name="LaTeX">
<input a0=""-\frac{\sqrt6-\sqrt2}{4}""/>
<output a0="cosz7"/>
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<condition showObject="hsmc ≟ "cos""/>
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SetBackgroundColor(cosz10,"蓝绿")
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<command name="LaTeX">
<input a0=""-\frac{1}{2}""/>
<output a0="cosz8"/>
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<element type="text" label="cosz8">
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<condition showObject="hsmc ≟ "cos""/>
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SetBackgroundColor(cosz4,"蓝绿")
SetBackgroundColor(cosz5,"蓝绿")
SetBackgroundColor(cosz6,"蓝绿")
SetBackgroundColor(cosz7,"蓝绿")
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SetBackgroundColor(cosz4,"蓝绿")
SetBackgroundColor(cosz5,"蓝绿")
SetBackgroundColor(cosz6,"蓝绿")
SetBackgroundColor(cosz7,"蓝绿")
SetBackgroundColor(cosz8,"蓝绿")
SetBackgroundColor(cosz9,"蓝绿")
SetBackgroundColor(cosz10,"蓝绿")
SetBackgroundColor(cosz11,"蓝绿")
SetBackgroundColor(cosz12,"蓝绿")
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<command name="LaTeX">
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<output a0="cosz10"/>
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<element type="text" label="cosz10">
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<condition showObject="hsmc ≟ "cos""/>
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SetBackgroundColor(cosz7,"蓝绿")
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SetBackgroundColor(cosz9,"蓝绿")
SetBackgroundColor(cosz10,"蓝绿")
SetBackgroundColor(cosz11,"蓝绿")
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<command name="LaTeX">
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<output a0="cosz11"/>
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SetBackgroundColor(cosz4,"蓝绿")
SetBackgroundColor(cosz5,"蓝绿")
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<command name="LaTeX">
<input a0=""-1""/>
<output a0="cosz12"/>
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<element type="text" label="cosz12">
<show object="false" label="true" ev="8"/>
<condition showObject="hsmc ≟ "cos""/>
<objColor r="128" g="0" b="0" alpha="0"/>
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<command name="RandomElement">
<input a0="{"sin", "cos"}"/>
<output a0="hsmc"/>
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<element type="text" label="hsmc">
<symbolic val="true" />
<show object="false" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
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<startPoint x="-2.100000000000001" y="0.4999999999999998" z="1"/>
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<element type="boolean" label="isSin">
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<show object="true" label="true"/>
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<checkbox fixed="true"/>
<caption val="正弦"/>
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SetValue(txtSel,"")
SetValue(isTiShi,false)
SetValue(txtVerIf,"选择答案后点“验证”")
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SetBackgroundColor(sinz0,"蓝绿")
SetBackgroundColor(sinz1,"蓝绿")
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SetBackgroundColor(sinf1,"蓝绿")
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SetBackgroundColor(sinf3,"蓝绿")
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SetBackgroundColor(tanz0,"蓝绿")
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SetBackgroundColor(tanf1,"蓝绿")
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SetBackgroundColor(tanf4,"蓝绿")
SetBackgroundColor(tanf5,"蓝绿")
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<show object="true" label="false"/>
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<ggbscript onUpdate="SetCaption(%0,If(%0==0,"起始弧度：0","起始弧度："+%0+"π")) "/>
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<element type="numeric" label="cycles">
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<show object="true" label="false"/>
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<command name="LaTeX">
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<element type="text" label="showa">
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<show object="true" label="true" ev="8"/>
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<element type="text" label="txtVerIf">
<show object="true" label="true" ev="40"/>
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<element type="text" label="txtSel">
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<command name="If">
<input a0="numas12 ≥ 0" a1=""sinz" + numas12" a2=""sinf" + (abs(numas12))"/>
<output a0="nameSin"/>
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<element type="text" label="nameSin">
<show object="false" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
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<command name="Mod">
<input a0="numa" a1="24"/>
<output a0="numac24"/>
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<element type="numeric" label="numac24">
<value val="1"/>
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<command name="If">
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<output a0="numac12"/>
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<expression label="nameCos" exp=""cosz" + numac12" />
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<expression label="txt标题" exp=""特殊角的三角函数值""/>
<element type="text" label="txt标题">
<show object="true" label="true" ev="40"/>
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<fixed val="true"/>
<isLaTeX val="true"/>
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<command name="Circle">
<input a0="Intersect[xAxis, yAxis]" a1="1"/>
<output a0="c"/>
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<element type="conic" label="c">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
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<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
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<font serif="false" sizeM="1.4" size="5" style="1"/>
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<ggbscript val="SetBackgroundColor(tanz0,"蓝绿")
SetBackgroundColor(tanz1,"蓝绿")
SetBackgroundColor(tanz2,"蓝绿")
SetBackgroundColor(tanz3,"蓝绿")
SetBackgroundColor(tanz4,"蓝绿")
SetBackgroundColor(tanz5,"蓝绿")
SetBackgroundColor(tan6,"蓝绿")
SetBackgroundColor(tanf1,"蓝绿")
SetBackgroundColor(tanf2,"蓝绿")
SetBackgroundColor(tanf3,"蓝绿")
SetBackgroundColor(tanf4,"蓝绿")
SetBackgroundColor(tanf5,"蓝绿")
SetBackgroundColor(%0,"红色")
SetValue(txtSel,Name(%0))"/>
</element>
<command name="LaTeX">
<input a0=""\sqrt3"" a1="true" a2="true"/>
<output a0="tanz4"/>
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<element type="text" label="tanz4">
<show object="true" label="true" ev="8"/>
<condition showObject="hsmc ≟ "tan""/>
<objColor r="0" g="0" b="0" alpha="0"/>
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<font serif="false" sizeM="1.4" size="5" style="1"/>
<auxiliary val="true"/>
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SetBackgroundColor(tanz1,"蓝绿")
SetBackgroundColor(tanz2,"蓝绿")
SetBackgroundColor(tanz3,"蓝绿")
SetBackgroundColor(tanz4,"蓝绿")
SetBackgroundColor(tanz5,"蓝绿")
SetBackgroundColor(tan6,"蓝绿")
SetBackgroundColor(tanf1,"蓝绿")
SetBackgroundColor(tanf2,"蓝绿")
SetBackgroundColor(tanf3,"蓝绿")
SetBackgroundColor(tanf4,"蓝绿")
SetBackgroundColor(tanf5,"蓝绿")
SetBackgroundColor(%0,"红色")
SetValue(txtSel,Name(%0))"/>
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<command name="LaTeX">
<input a0=""2+\sqrt3"" a1="true" a2="true"/>
<output a0="tanz5"/>
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<element type="text" label="tanz5">
<show object="true" label="true" ev="8"/>
<condition showObject="hsmc ≟ "tan""/>
<objColor r="0" g="0" b="0" alpha="0"/>
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<isLaTeX val="true"/>
<font serif="false" sizeM="1.4" size="5" style="1"/>
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<absoluteScreenLocation x="317" y="107"/>
<ggbscript val="SetBackgroundColor(tanz0,"蓝绿")
SetBackgroundColor(tanz1,"蓝绿")
SetBackgroundColor(tanz2,"蓝绿")
SetBackgroundColor(tanz3,"蓝绿")
SetBackgroundColor(tanz4,"蓝绿")
SetBackgroundColor(tanz5,"蓝绿")
SetBackgroundColor(tan6,"蓝绿")
SetBackgroundColor(tanf1,"蓝绿")
SetBackgroundColor(tanf2,"蓝绿")
SetBackgroundColor(tanf3,"蓝绿")
SetBackgroundColor(tanf4,"蓝绿")
SetBackgroundColor(tanf5,"蓝绿")
SetBackgroundColor(%0,"红色")
SetValue(txtSel,Name(%0))"/>
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<command name="Mod">
<input a0="numa" a1="12"/>
<output a0="numat12"/>
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<element type="numeric" label="numat12">
<value val="1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
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<command name="If">
<input a0="numat12 > 6" a1="numat12 - 12" a2="numat12"/>
<output a0="numat6"/>
</command>
<element type="numeric" label="numat6">
<value val="1"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
</element>
<command name="If">
<input a0="abs(numat6) ≟ 6" a1=""tan6"" a2="If[numat6 ≥ 0, ("tanz" * numat6), ("tanf" * abs(numat6))]"/>
<output a0="nameTan"/>
</command>
<element type="text" label="nameTan">
<show object="false" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
</element>
<command name="LaTeX">
<input a0=""0""/>
<output a0="cosz6"/>
</command>
<element type="text" label="cosz6">
<show object="false" label="true" ev="8"/>
<condition showObject="hsmc ≟ "cos""/>
<objColor r="128" g="0" b="0" alpha="0.10000000149011612"/>
<bgColor r="175" g="238" b="238" alpha="255"/>
<layer val="0"/>
<labelMode val="1"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.4" size="5" style="1"/>
<auxiliary val="true"/>
<absoluteScreenLocation x="425" y="324"/>
<ggbscript val="SetBackgroundColor(cosz0,"蓝绿")
SetBackgroundColor(cosz1,"蓝绿")
SetBackgroundColor(cosz2,"蓝绿")
SetBackgroundColor(cosz3,"蓝绿")
SetBackgroundColor(cosz4,"蓝绿")
SetBackgroundColor(cosz5,"蓝绿")
SetBackgroundColor(cosz6,"蓝绿")
SetBackgroundColor(cosz7,"蓝绿")
SetBackgroundColor(cosz8,"蓝绿")
SetBackgroundColor(cosz9,"蓝绿")
SetBackgroundColor(cosz10,"蓝绿")
SetBackgroundColor(cosz11,"蓝绿")
SetBackgroundColor(cosz12,"蓝绿")
SetBackgroundColor(%0,"红色")
SetValue(txtSel,Name(%0))"/>
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<command name="LaTeX">
<input a0=""1""/>
<output a0="cosz0"/>
</command>
<element type="text" label="cosz0">
<show object="false" label="true" ev="8"/>
<condition showObject="hsmc ≟ "cos""/>
<objColor r="128" g="0" b="0" alpha="0"/>
<bgColor r="175" g="238" b="238" alpha="255"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="1.4" size="5" style="1"/>
<auxiliary val="true"/>
<absoluteScreenLocation x="425" y="248"/>
<ggbscript val="SetBackgroundColor(cosz0,"蓝绿")
SetBackgroundColor(cosz1,"蓝绿")
SetBackgroundColor(cosz2,"蓝绿")
SetBackgroundColor(cosz3,"蓝绿")
SetBackgroundColor(cosz4,"蓝绿")
SetBackgroundColor(cosz5,"蓝绿")
SetBackgroundColor(cosz6,"蓝绿")
SetBackgroundColor(cosz7,"蓝绿")
SetBackgroundColor(cosz8,"蓝绿")
SetBackgroundColor(cosz9,"蓝绿")
SetBackgroundColor(cosz10,"蓝绿")
SetBackgroundColor(cosz11,"蓝绿")
SetBackgroundColor(cosz12,"蓝绿")
SetBackgroundColor(%0,"红色")
SetValue(txtSel,Name(%0))"/>
</element>
<element type="boolean" label="isTiShi">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="27" y="371"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
<caption val="提示"/>
</element>
<expression label="text1" exp=""起始弧度""/>
<element type="text" label="text1">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="1.4" size="5" style="0"/>
<absoluteScreenLocation x="26" y="137"/>
</element>
<expression label="text2" exp=""周期跨度""/>
<element type="text" label="text2">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<font serif="false" sizeM="1.4" size="5" style="0"/>
<absoluteScreenLocation x="26" y="175"/>
</element>
<expression label="text3" exp=""" + (If[starta ≟ 0, "0", (starta * " π ")]) + """ />
<element type="text" label="text3">
<show object="true" label="true" ev="40"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<font serif="true" sizeM="1.4" size="5" style="1"/>
<absoluteScreenLocation x="236" y="137"/>
</element>
<expression label="text4" exp=""" + (LaTeX[(FractionText[(cycles * 2)] * π)]) + """ />
<element type="text" label="text4">
<show object="true" label="true" ev="8"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="5" style="0"/>
<absoluteScreenLocation x="231" y="150"/>
</element>
<expression label="lbResults" exp="{{"题号", "题目", "回答", "验证"}, {"1", "\cos \frac{ 1 }{ 2 } π ", "0", "true"}, {"2", "\sin \frac{ 7 }{ 4 } π ", "-\frac{\sqrt2}{2}", "true"}, {"3", "\cos \frac{ 7 }{ 12 } π ", "\frac{\sqrt6-\sqrt2}{4}", "false"}, {"4", "\tan \frac{ 1 }{ 12 } π ", "2-\sqrt3", "true"}}"/>
<element type="list" label="lbResults">
<show object="false" label="false"/>
<objColor r="0" g="100" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="0" playing="false"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
</element>
<element type="button" label="btnReset">
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="635" y="11"/>
<labelMode val="3"/>
<fixed val="true"/>
<auxiliary val="true"/>
<ggbscript val="SetValue(count,0)
SetValue(numTrue,0)
SetValue(lbResults,{{"题号","题目","回答","验证"}})
SetValue(showa,"")
SetValue(txtResults,LaTeX("$问题数：0\\正确数：0\\正确率：0%$",true,true))"/>
<caption val="重置统计数据"/>
</element>
<element type="numeric" label="count">
<value val="4"/>
<symbolic val="true" />
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="100" absoluteScreenLocation="true" width="200" fixed="false" horizontal="true" showAlgebra="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<element type="numeric" label="numTrue">
<value val="3"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="0" max="100" absoluteScreenLocation="true" width="200" fixed="false" horizontal="true" showAlgebra="false"/>
<lineStyle thickness="2" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<expression label="txtResults" exp=""$问题数：4\\正确数：3\\正确率：75\%$""/>
<element type="text" label="txtResults">
<show object="true" label="true" ev="40"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="3"/>
<fixed val="true"/>
<isLaTeX val="true"/>
<font serif="true" sizeM="1.4" size="5" style="0"/>
<absoluteScreenLocation x="401" y="454"/>
</element>
<element type="boolean" label="isNew">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="300" y="526"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<checkbox fixed="true"/>
</element>
<command name="TableText">
<input a0="lbResults" a1=""|_c""/>
<output a0="txtLbResults"/>
</command>
<element type="text" label="txtLbResults">
<show object="true" label="true" ev="8"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<isLaTeX val="true"/>
<font serif="false" sizeM="0.7" size="-4" style="0"/>
<absoluteScreenLocation x="620" y="57"/>
</element>
<command name="If">
<input a0="hsmc ≟ "sin"" a1="txtSel ≟ nameSin" a2="If[hsmc ≟ "cos", txtSel ≟ nameCos, txtSel ≟ nameTan]"/>
<output a0="isRight"/>
</command>
<element type="boolean" label="isRight">
<value val="false"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<checkbox fixed="true"/>
</element>
<expression label="lbResult" exp="{LaTeX[count], LaTeX[showa], LaTeX[Object[txtSel]], LaTeX[isRight]}" />
<element type="list" label="lbResult">
<show object="false" label="false" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="0"/>
<lineStyle thickness="5" type="0" typeHidden="1"/>
<pointSize val="5"/>
<angleStyle val="0"/>
<symbolic val="true" />
</element>
<command name="Segment">
<input a0="(0, 0)" a1="(cos((numa * π / 12)), sin((numa * π / 12)))"/>
<output a0="tiShi"/>
</command>
<element type="segment" label="tiShi">
<show object="true" label="false" ev="4"/>
<condition showObject="isTiShi"/>
<objColor r="0" g="0" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
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<lineStyle thickness="9" type="30" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
</construction>
</geogebra>