正弦函数图像的绘制与动态演示
2020-03-10 00:20
本范例展示了正弦函数图像的绘制过程。通过GeoGebra的CurveCartesian等命令，结合参数方程与几何构造，动态呈现正弦曲线的生成原理。包含点、射线、角度及线段等几何对象的交互，帮助直观理解三角函数的周期性、振幅及相位变化，适用于三角函数与函数图像的教学演示。
所属专题
中职数学GeoGebra互动教学资源库
<?xml version="1.0" encoding="utf-8"?>
<geogebra format="5.0" version="5.0.574.0" app="classic" platform="w" id="0fac617c-ddd4-47d5-9259-3113f6126113" xsi:noNamespaceSchemaLocation="http://www.geogebra.org/apps/xsd/ggb.xsd" xmlns="" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" >
<gui>
<window width="700" height="284" />
<perspectives>
<perspective id="tmp">
<panes>
<pane location="" divider="0" orientation="1" />
</panes>
<views>
<view id="512" toolbar="0 | 1 501 5 19 , 67 | 2 15 45 18 , 7 37 | 514 3 9 , 13 44 , 47 | 16 51 | 551 550 11 , 20 22 21 23 , 55 56 57 , 12 | 69 | 510 511 , 512 513 | 533 531 , 534 532 , 522 523 , 537 536 , 535 | 521 520 | 36 , 38 49 560 | 571 30 29 570 31 33 | 17 | 540 40 41 42 , 27 28 35 , 6 , 502" visible="false" inframe="false" stylebar="false" location="1,1,1" size="500" window="100,100,600,400" />
<view id="4" toolbar="0 || 2020 , 2021 , 2022 , 66 || 2001 , 2003 , 2002 , 2004 , 2005 || 2040 , 2041 , 2042 , 2044 , 2043" visible="false" inframe="false" stylebar="false" location="1,1" size="300" window="100,100,600,400" />
<view id="8" toolbar="1001 | 1002 | 1003 || 1005 | 1004 || 1006 | 1007 | 1010 || 1008 1009 || 66 68 || 6" visible="false" inframe="false" stylebar="false" location="1,3" size="300" window="100,100,600,400" />
<view id="4097" visible="false" inframe="false" stylebar="true" location="1,1" size="331" window="100,100,700,550" />
<view id="1" visible="true" inframe="false" stylebar="false" location="1" size="690" window="100,100,600,400" />
<view id="2" visible="true" inframe="false" stylebar="false" location="3" size="0" window="100,100,600,400" />
<view id="16" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="32" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="64" toolbar="0" visible="false" inframe="false" stylebar="false" location="1" size="150" window="50,50,500,500" />
<view id="128" visible="false" inframe="false" stylebar="false" location="1" size="480" window="50,50,500,500" />
<view id="70" toolbar="0 || 2020 || 2021 || 2022" visible="false" inframe="false" stylebar="true" location="1" size="150" window="50,50,500,500" />
<view id="43" visible="false" inframe="false" stylebar="false" location="1" size="450" window="50,50,500,500" />
</views>
<toolbar show="false" items="0 39 73 62 | 1 501 67 , 5 19 , 72 75 76 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24 20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49 50 , 71 14 68 | 30 29 54 32 31 33 | 25 17 26 60 52 61 | 40 41 42 , 27 28 35 , 6" position="1" help="false" />
<input show="false" cmd="true" top="algebra" />
<dockBar show="false" east="false" />
</perspective>
</perspectives>
<labelingStyle val="0"/>
<font size="12"/>
</gui>
<euclidianView>
<viewNumber viewNo="1"/>
<size width="689" height="281"/>
<coordSystem xZero="159.71159792954194" yZero="154.93134205047514" scale="46.26961789866992" yscale="46.26961789867004"/>
<evSettings axes="true" grid="false" gridIsBold="false" pointCapturing="3" rightAngleStyle="1" checkboxSize="26" gridType="3"/>
<bgColor r="255" g="255" b="255"/>
<axesColor r="0" g="0" b="0"/>
<gridColor r="192" g="192" b="192"/>
<lineStyle axes="1" grid="0"/>
<axis id="0" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true" tickDistance="1.5707963267948966" tickExpression="π / 2"/>
<axis id="1" show="true" label="" unitLabel="" tickStyle="1" showNumbers="true"/>
</euclidianView>
<algebraView>
<mode val="3"/>
<auxiliary show="true"/>
</algebraView>
<kernel>
<continuous val="false"/>
<usePathAndRegionParameters val="true"/>
<decimals val="2"/>
<angleUnit val="degree"/>
<algebraStyle val="0" spreadsheet="0"/>
<coordStyle val="0"/>
</kernel>
<tableview min="-2" max="2" step="1"/>
<scripting blocked="false" disabled="false"/>
<construction title="" author="" date="">
<element type="angle" label="k'">
<angleStyle val="3"/>
<value val="1.0456385338492589"/>
<slider min="0" max="6.283185307179586" absoluteScreenLocation="true" width="180" x="60" y="40" fixed="false" horizontal="true" showAlgebra="true"/>
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="10" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
<animation speed="1" type="0" playing="false"/>
</element>
<expression label="c" exp="(x + 1)^(2) + y^(2) = 1" type="conic"/>
<element type="conic" label="c">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="153" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<eigenvectors x0="1" y0="0" z0="1.0" x1="0" y1="1" z1="1.0"/>
<matrix A0="1" A1="1" A2="0" A3="0" A4="1" A5="0"/>
<eqnStyle style="specific"/>
</element>
<command name="Point">
<input a0="c"/>
<output a0="P"/>
</command>
<element type="point" label="P">
<show object="true" label="true" ev="4"/>
<objColor r="125" g="125" b="255" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="true"/>
<ggbscript onUpdate="SetValue[k',k]
"/>
<coords x="-0.462210740904088" y="0.8430793039809897" z="1"/>
<pointSize val="5"/>
<pointStyle val="0"/>
</element>
<element type="numeric" label="count">
<value val="1"/>
<show object="false" label="true"/>
<objColor r="0" g="0" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<slider min="-10" max="10" absoluteScreenLocation="true" width="200" x="71" y="73" fixed="false" horizontal="true" showAlgebra="true"/>
<lineStyle thickness="10" type="0" typeHidden="1"/>
<animation step="1" speed="1" type="0" playing="false"/>
</element>
<command name="Angle">
<input a0="(0, 0)" a1="(-1, 0)" a2="P"/>
<output a0="k"/>
</command>
<element type="angle" label="k">
<angleStyle val="0"/>
<value val="1.002983638926863"/>
<show object="false" label="true" ev="4"/>
<objColor r="0" g="100" b="0" alpha="0.10000000149011612"/>
<layer val="0"/>
<labelMode val="1"/>
<lineStyle thickness="5" type="0" typeHidden="2" opacity="178"/>
<arcSize val="30"/>
</element>
<expression label="pass1" exp="k - k' < (-(200°))" />
<element type="boolean" label="pass1">
<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"/>
<ggbscript onUpdate="SetValue[count,If[pass1,count+1,count]]"/>
</element>
<expression label="pass2" exp="k - k' > 200°" />
<element type="boolean" label="pass2">
<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"/>
<ggbscript onUpdate="SetValue[count,If[pass2,count-1,count]]"/>
</element>
<expression label="theta" exp="k' + (360° * count)" />
<element type="angle" label="theta">
<angleStyle val="3"/>
<value val="7.328823841028845"/>
</element>
<expression label="r" exp="r(x) = 0.25 + (0.75 * (1 - ℯ^(((-abs(x))) / ((12 * π)))))" type="function"/>
<element type="function" label="r">
<show object="false" label="true" ev="4"/>
<objColor r="204" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<fixed val="true"/>
<auxiliary val="true"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
</element>
<expression label="A" exp="(-1, 0)" type="point"/>
<element type="point" label="A">
<show object="false" label="true" ev="4"/>
<objColor r="68" g="68" b="68" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<animation step="0.1" speed="1" type="1" playing="false"/>
<auxiliary val="true"/>
<coords x="-1" y="0" z="1"/>
<pointSize val="4"/>
<pointStyle val="0"/>
</element>
<command name="Ray">
<input a0="A" a1="P"/>
<output a0="f"/>
</command>
<element type="ray" label="f">
<show object="true" label="false" ev="4"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<coords x="-0.8430793039809897" y="0.537789259095912" z="-0.8430793039809897"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="CurveCartesian">
<input a0="(r(t) * cos(t)) - 1" a1="(r(t) * sin(t))" a2="t" a3="Min[0, theta]" a4="Max[0, theta]"/>
<output a0="a"/>
</command>
<element type="curvecartesian" label="a">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<auxiliary val="true"/>
<lineStyle thickness="2" type="0" typeHidden="1" opacity="178"/>
</element>
<command name="CurveCartesian">
<input a0="t" a1="sin(t)" a2="t" a3="Min[0, theta]" a4="Max[0, theta]"/>
<output a0="b"/>
</command>
<element type="curvecartesian" label="b">
<show object="true" label="true" ev="4"/>
<objColor r="102" g="0" b="153" alpha="0"/>
<layer val="0"/>
<labelOffset x="-6" y="-27"/>
<labelMode val="0"/>
<lineStyle thickness="7" type="0" typeHidden="1" opacity="178"/>
</element>
<command name="Segment">
<input a0="P" a1="((theta * π / (180°)), sin((theta * π / (180°))))"/>
<output a0="g"/>
</command>
<element type="segment" label="g">
<show object="true" label="true" ev="4"/>
<objColor r="0" g="51" b="153" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="-0.02216553899319673" y="7.791034581932933" z="-6.578705162828422"/>
<lineStyle thickness="5" type="10" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<command name="Segment">
<input a0="P" a1="(x(P), 0)"/>
<output a0="h"/>
</command>
<element type="segment" label="h">
<show object="true" label="true" ev="4"/>
<objColor r="255" g="51" b="204" alpha="0"/>
<layer val="0"/>
<labelMode val="0"/>
<coords x="0.8430793039809897" y="0" z="0.38968030973395607"/>
<lineStyle thickness="5" type="0" typeHidden="1" opacity="178"/>
<outlyingIntersections val="false"/>
<keepTypeOnTransform val="true"/>
</element>
<expression label="text1" exp="("角度：" * theta)" />
<element type="text" label="text1">
<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="true" sizeM="1" size="0" style="0"/>
<startPoint x="0.4920040861522499" y="1.8952675080958878" z="1"/>
</element>
<element type="boolean" label="isStart">
<value val="false"/>
<show object="true" label="true"/>
<objColor r="0" g="0" b="0" alpha="0"/>
<layer val="0"/>
<labelOffset x="45" y="18"/>
<labelMode val="3"/>
<checkbox fixed="true"/>
<ggbscript onUpdate="StartAnimation[isStart]"/>
<caption val="启动动画"/>
</element>
<expression label="text2" exp=""操作提示：点击【启动动画】复选框，或拖动点P观察图像的正弦函数的绘制。""/>
<element type="text" label="text2">
<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"/>
<absoluteScreenLocation x="220" y="33"/>
</element>
</construction>
</geogebra>