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<b>let </b><font color="Maroon">c<sub>1</sub></font> be  <a href="xreal_0.html#V1">real</a>  <a href="ordinal1.html#NM1" target="_self">number</a> ;<br/>

<b>assume </b><b>that </b><br/><a NAME="E1:29"/><i><font color="Green">E56</font></i>: 
0 <a href="xxreal_0.html#R1">&lt;=</a> <font color="Maroon">c<sub>1</sub></font>
 <b>and </b><br/><a NAME="E2:29"/><i><font color="Green">E57</font></i>: 
<font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;=</a> 2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> 
 <b>and </b><br/><a NAME="E3:29"/><i><font color="Green">E58</font></i>: 
 <a href="sin_cos.html#K20">sin</a> <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a>  <a href="real_1.html#K1">-</a> 1
 ;<br/>

<a NAME="E4:29"/><i><font color="Green">E59</font></i>: 
( <font color="Maroon">c<sub>1</sub></font> <a href="hidden.html#R1">=</a> 2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a>  or <font color="Maroon">c<sub>1</sub></font> <a href="xxreal_0.html#R1">&lt;</a> 2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a>  )
 
<b>by </b><i><a class="txt" href="sin_cos6.html#E2:29"><i><font color="Green">E57</font></i></a>, <a class="ref" href="real_1.html#D5">REAL_1:def 5</a></i>;<br/>
<b>thus </b><font color="Maroon">c<sub>1</sub></font> = 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="xcmplx_0.html#K2">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="xcmplx_0.html#K3">*</a> <span class="p2"><a href="int_1.html#K1">[\</a><span class="default"><span class="p3">(<span class="default"><font color="Maroon">c<sub>1</sub></font> <a href="xcmplx_0.html#K7">/</a> <span class="p4">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span></span>)</span></span><a href="int_1.html#K1">/]</a></span></span>)</span>
<b>by </b><i><a class="txt" href="sin_cos6.html#E3:29"><i><font color="Green">E58</font></i></a>, <a class="ref" href="sin_cos6.html#T23" target="_self">Th23</a></i>
<br/>.= 
<span class="p1">(<span class="default"><span class="p2">(<span class="default">3 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="real_1.html#K3">+</a> <span class="p1">(<span class="default"><span class="p2">(<span class="default">2 <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> </span>)</span> <a href="real_1.html#K4">*</a> 0</span>)</span>
<b>by </b><i><a class="txt" href="sin_cos6.html#E1:29"><i><font color="Green">E56</font></i></a>, <a class="txt" href="sin_cos6.html#E3:29"><i><font color="Green">E58</font></i></a>, <a class="txt" href="sin_cos6.html#E4:29"><i><font color="Green">E59</font></i></a>, <a class="ref" href="sin_cos6.html#T1" target="_self">Th1</a>, <a class="ref" href="sin_cos.html#T82">SIN_COS:82</a></i>
<br/>.= 
<span class="p1">(<span class="default">3 <a href="real_1.html#K6">/</a> 2</span>)</span> <a href="real_1.html#K4">*</a> <a href="sin_cos.html#K33">PI</a> 

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