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EMMentor online - Independent problem solving - Trigonometry Equations
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<table width="262" ><tr><td width="150" background="../../../../button/menu_bg.gif"><b>Test</b></td><td width="24" class="tableh1"><div align="center"><a href="../0/v0.xml" target="_parent"><b><font color="FF9900">1</font></b></a></div></td><td width="24" class="tableh1"><div align="center"><a href="../0/v1.xml" target="_parent"><b>2</b></a></div></td><td width="24" class="tableh1"><div align="center"><a href="../1/v0.xml" target="_parent"><b>3</b></a></div></td><td width="24" class="tableh1"><div align="center"><a href="../1/v1.xml" target="_parent"><b>4</b></a></div></td><td width="24" class="tableh1"><div align="center"><a href="../2/v0.xml" target="_parent"><b>5</b></a></div></td><td width="24" class="tableh1"><div align="center"><a href="../2/v1.xml" target="_parent"><b>6</b></a></div></td></tr></table>
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<p><b>
<font color="FF9900">
Test - 1
</font>
</b></p>
<p><b>Example - 2</b></p>
<a name="pont0">
<b>Solve the equation</b>
</a>
<table width="100%">
<tr>
<td>
<a href="jawascript:void(0)" onClick="window.open('../sub/1.xml','WindowName','width=650,height=550,scrollbars=yes,resizable=yes,toolbar=no,status=no'); return false;">
<img src="../image/detail.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><msup><mi>sin</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mrow><mi>3 </mi><mi>s</mi></mrow></mrow>
</mrow></mfenced></mrow>
<mo>+</mo>
<mrow><msup><mi>sin</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mrow><mi>s</mi></mrow></mrow>
</mrow></mfenced></mrow>
<mo>=</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</math>
</td>
</tr>
</table>
<a name="pont1">
<p>1. Let's apply the formula of sum of sines</p>
</a>
<table width="100%">
<tr>
<td>
<a href="jawascript:void(0)" onClick="window.open('../sub/181.xml','WindowName','width=650,height=550,scrollbars=yes,resizable=yes,toolbar=no,status=no'); return false;">
<img src="../image/detail.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><mrow><mi>2 </mi></mrow></mrow>
<mo>&#x00B7;</mo>
<mrow><msup><mi>sin</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mfrac>
<mrow>
<mrow><mrow><mi>3 </mi><mi>s</mi></mrow><mrow><mo>+</mo><mi>s</mi></mrow></mrow>
</mrow>
<mrow>
<mrow><mrow><mi>2 </mi></mrow></mrow>
</mrow></mfrac></mrow>
</mrow></mfenced></mrow>
<mo>&#x00B7;</mo>
<mrow><msup><mi>cos</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mfrac>
<mrow>
<mrow><mrow><mi>3 </mi><mi>s</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>s</mi></mrow></mrow>
</mrow>
<mrow>
<mrow><mrow><mi>2 </mi></mrow></mrow>
</mrow></mfrac></mrow>
</mrow></mfenced></mrow>
<mo>=</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</math>
</td>
</tr>
</table>
<a name="pont2">
<p>2. Let's divide both sides of expression by the numeric factor</p>
</a>
<table width="100%">
<tr>
<td>
<a href="jawascript:void(0)" onClick="window.open('../sub/30.xml','WindowName','width=650,height=550,scrollbars=yes,resizable=yes,toolbar=no,status=no'); return false;">
<img src="../image/detail.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><msup><mi>sin</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mfrac>
<mrow>
<mrow><mrow><mi>3 </mi><mi>s</mi></mrow><mrow><mo>+</mo><mi>s</mi></mrow></mrow>
</mrow>
<mrow>
<mrow><mrow><mi>2 </mi></mrow></mrow>
</mrow></mfrac></mrow>
</mrow></mfenced></mrow>
<mo>&#x00B7;</mo>
<mrow><msup><mi>cos</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mfrac>
<mrow>
<mrow><mrow><mi>3 </mi><mi>s</mi></mrow><mrow><mo>&#x002D;&#x00A0;</mo><mi>s</mi></mrow></mrow>
</mrow>
<mrow>
<mrow><mrow><mi>2 </mi></mrow></mrow>
</mrow></mfrac></mrow>
</mrow></mfenced></mrow>
<mo>=</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</math>
</td>
</tr>
</table>
<a name="pont3">
<p>3. Let's add up coefficients at the like terms</p>
</a>
<table width="100%">
<tr>
<td>
<a href="jawascript:void(0)" onClick="window.open('../sub/8.xml','WindowName','width=650,height=550,scrollbars=yes,resizable=yes,toolbar=no,status=no'); return false;">
<img src="../image/detail.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><msup><mi>sin</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mfrac>
<mrow>
<mrow><mrow><mi>4 </mi><mi>s</mi></mrow></mrow>
</mrow>
<mrow>
<mrow><mrow><mi>2 </mi></mrow></mrow>
</mrow></mfrac></mrow>
</mrow></mfenced></mrow>
<mo>&#x00B7;</mo>
<mrow><msup><mi>cos</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mfrac>
<mrow>
<mrow><mrow><mi>2 </mi><mi>s</mi></mrow></mrow>
</mrow>
<mrow>
<mrow><mrow><mi>2 </mi></mrow></mrow>
</mrow></mfrac></mrow>
</mrow></mfenced></mrow>
<mo>=</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</math>
</td>
</tr>
</table>
<a name="pont4">
<p>4. Let us reduce fraction, using the distributive law and the main property of fraction</p>
</a>
<table width="100%">
<tr>
<td>
<a href="jawascript:void(0)" onClick="window.open('../sub/77.xml','WindowName','width=650,height=550,scrollbars=yes,resizable=yes,toolbar=no,status=no'); return false;">
<img src="../image/detail.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><msup><mi>sin</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mrow><mi>2 </mi><mi>s</mi></mrow></mrow>
</mrow></mfenced></mrow>
<mo>&#x00B7;</mo>
<mrow><msup><mi>cos</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mfrac>
<mrow>
<mrow><mrow><mi>2 </mi><mi>s</mi></mrow></mrow>
</mrow>
<mrow>
<mrow><mrow><mi>2 </mi></mrow></mrow>
</mrow></mfrac></mrow>
</mrow></mfenced></mrow>
<mo>=</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</math>
</td>
</tr>
</table>
<a name="pont5">
<p>5. Let us reduce fraction, using the distributive law and the main property of fraction</p>
</a>
<table width="100%">
<tr>
<td>
<a href="jawascript:void(0)" onClick="window.open('../sub/77.xml','WindowName','width=650,height=550,scrollbars=yes,resizable=yes,toolbar=no,status=no'); return false;">
<img src="../image/detail.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow>
<mrow>
<mrow><msup><mi>sin</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mrow><mi>2 </mi><mi>s</mi></mrow></mrow>
</mrow></mfenced></mrow>
<mo>&#x00B7;</mo>
<mrow><msup><mi>cos</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mrow><mi>s</mi></mrow></mrow>
</mrow></mfenced></mrow>
<mo>=</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</math>
</td>
</tr>
</table>
<a name="pont6">
<p>6. Using properties of product, let us replace the equation(s) by the aggregation of equations</p>
</a>
<table width="100%">
<tr>
<td>
<a href="jawascript:void(0)" onClick="window.open('../sub/401.xml','WindowName','width=650,height=550,scrollbars=yes,resizable=yes,toolbar=no,status=no'); return false;">
<img src="../image/detail.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>[</mo>
<mtable>
<mtr>
<mtd align="left">
<mrow>
<mrow>
<mrow><msup><mi>sin</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mrow><mi>2 </mi><mi>s</mi></mrow></mrow>
</mrow></mfenced></mrow>
<mo>=</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</mtd>
</mtr>
<mtr>
<mtd align="left">
<mrow>
<mrow>
<mrow><msup><mi>cos</mi>
<mrow>

</mrow></msup>
<mfenced><mrow>
<mrow><mrow><mi>s</mi></mrow></mrow>
</mrow></mfenced></mrow>
<mo>=</mo>
<mrow><mrow><mi>0 </mi></mrow></mrow>
</mrow>
</mrow>
</mtd>
</mtr>
</mtable>
</mrow>
</math>
</td>
</tr>
</table>
<a name="pont7">
<p>7. Let us apply the inversion formulas</p>
</a>
<table width="100%">
<tr>
<td>
<a href="jawascript:void(0)" onClick="window.open('../sub/329.xml','WindowName','width=650,height=550,scrollbars=yes,resizable=yes,toolbar=no,status=no'); return false;">
<img src="../image/detail.gif"  border="0" align="absmiddle" alt="detail"></img></a>
</td>
<td width="95%">
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mo>[</mo>
<mtable>
<mtr>
<mtd align="left">
<mrow>
<mrow>
<mrow><mrow><mi>s</mi></mrow></mrow>
<mo>=</mo>
<mrow><mrow><mfrac><mi>&#x03C0;</mi><mi>2</mi></mfrac></mrow></mrow>
<mo>&#x00B7;</mo>
<mrow><mrow><mi>k</mi></mrow></mrow>
<mi>&#x00A0;;&#x00A0;&#x00A0;</mi>
<mrow><mrow><mi>k</mi></mrow></mrow>
<mo>&#x2208;</mo>
<mrow><mrow><mi>Z</mi></mrow></mrow>
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<mrow><mrow><mi>s</mi></mrow></mrow>
<mo>=</mo>
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<mo>+</mo>
<mrow><mrow><mi>&#x03C0; </mi><mi>k</mi></mrow></mrow>
<mi>&#x00A0;;&#x00A0;&#x00A0;</mi>
<mrow><mrow><mi>k</mi></mrow></mrow>
<mo>&#x2208;</mo>
<mrow><mrow><mi>Z</mi></mrow></mrow>
</mrow>
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