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<div><span class="kw">theorem </span><a NAME="T28"><span class="comment"><font color="firebrick">:: TAYLOR_2:28</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">r</font>, <font color="Olive" title="b2">x</font> being   <a href="xreal_0.html#NM1" title="XREAL_0:NM.1">Real</a>  st <font color="Olive" title="b1">r</font> <a href="xxreal_0.html#NR4" title="XXREAL_0:NR.4">&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/>(  <a href="series_1.html#K3" title="SERIES_1:func.3">Partial_Sums</a> <span class="p1">(<span class="default"><a href="taylor_2.html#K1" title="TAYLOR_2:func.1">Maclaurin</a> (<a href="sin_cos.html#K16" title="SIN_COS:func.16">sin</a>,<span class="p2"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Olive" title="b1">r</font></span>)</span>,<font color="Olive" title="b1">r</font></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>,<font color="Olive" title="b2">x</font>)</span>)</span> is  <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>  &amp; <a href="sin_cos.html#K16" title="SIN_COS:func.16">sin</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p1">(<span class="default"><a href="taylor_2.html#K1" title="TAYLOR_2:func.1">Maclaurin</a> (<a href="sin_cos.html#K16" title="SIN_COS:func.16">sin</a>,<span class="p2"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Olive" title="b1">r</font></span>)</span>,<font color="Olive" title="b1">r</font></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>,<font color="Olive" title="b2">x</font>)</span>)</span> &amp;  <a href="series_1.html#K3" title="SERIES_1:func.3">Partial_Sums</a> <span class="p1">(<span class="default"><a href="taylor_2.html#K1" title="TAYLOR_2:func.1">Maclaurin</a> (<a href="sin_cos.html#K18" title="SIN_COS:func.18">cos</a>,<span class="p2"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Olive" title="b1">r</font></span>)</span>,<font color="Olive" title="b1">r</font></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>,<font color="Olive" title="b2">x</font>)</span>)</span> is  <a href="comseq_2.html#V2" title="COMSEQ_2:attr.2">convergent</a>  &amp; <a href="sin_cos.html#K18" title="SIN_COS:func.18">cos</a> <a href="funct_1.html#K1" title="FUNCT_1:func.1">.</a> <font color="Olive" title="b2">x</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="series_1.html#K4" title="SERIES_1:func.4">Sum</a> <span class="p1">(<span class="default"><a href="taylor_2.html#K1" title="TAYLOR_2:func.1">Maclaurin</a> (<a href="sin_cos.html#K18" title="SIN_COS:func.18">cos</a>,<span class="p2"><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">].</a><span class="default"><span class="p3">(<span class="default"><a href="xcmplx_0.html#K4" title="XCMPLX_0:func.4">-</a> <font color="Olive" title="b1">r</font></span>)</span>,<font color="Olive" title="b1">r</font></span><a href="rcomp_1.html#K2" title="RCOMP_1:func.2">.[</a></span>,<font color="Olive" title="b2">x</font>)</span>)</span> )</div></div>
