<?xml version="1.0"?>
<div><span class="kw">theorem </span><span class="lab"><font color="Green" title="E50">Th35</font></span>: <a NAME="T36"><span class="comment"><font color="firebrick">:: SIN_COS:36</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">th</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a> holds <br/> (  <a href="series_1.html#K3" title="SERIES_1:func.3">Partial_Sums</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">th</font> <a href="sin_cos.html#K20" title="SIN_COS:func.20">P_sin</a></span>)</span> is  <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>  &amp;  <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">th</font> <a href="sin_cos.html#K20" title="SIN_COS:func.20">P_sin</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K4" title="COMPLEX1:func.4">Im</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K11" title="COMSEQ_3:func.11">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">th</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a></span>)</span> <a href="sin_cos.html#K3" title="SIN_COS:func.3">ExpSeq</a></span>)</span></span>)</span> &amp;  <a href="series_1.html#K3" title="SERIES_1:func.3">Partial_Sums</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">th</font> <a href="sin_cos.html#K21" title="SIN_COS:func.21">P_cos</a></span>)</span> is  <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>  &amp;  <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p1">(<span class="default"><font color="Olive" title="b1">th</font> <a href="sin_cos.html#K21" title="SIN_COS:func.21">P_cos</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="complex1.html#K3" title="COMPLEX1:func.3">Re</a> <span class="p1">(<span class="default"><a href="comseq_3.html#K11" title="COMSEQ_3:func.11">Sum</a> <span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b1">th</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <a href="complex1.html#K7" title="COMPLEX1:func.7">&lt;i&gt;</a></span>)</span> <a href="sin_cos.html#K3" title="SIN_COS:func.3">ExpSeq</a></span>)</span></span>)</span> )</div></div>
