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<!--l. 92--><p class="noindent">The angle  <tspan font-family="cmmi" font-size="10"><img 
src="cmmi10-b.png" alt="a" class="10x-x-b" /></tspan> is 30<tspan baseline-shift="sub"><tspan font-family="cmsy" font-size="7"><span class="htf-cmbx">o</span></tspan>
 </tspan> in the example
(<tspan font-family="cmmi" font-size="10"><img 
src="cmmi10-19.png" alt="p" class="10x-x-19" />/</tspan>6 in radians). The sine of <tspan font-family="cmmi" font-size="10"><img 
src="cmmi10-b.png" alt="a" class="10x-x-b" /></tspan>,
which is the height of the red line,
is sin<tspan font-family="cmmi" font-size="10"><img 
src="cmmi10-b.png" alt="a" class="10x-x-b" /></tspan> =  1<tspan font-family="cmmi" font-size="10">/</tspan>2<tspan font-family="cmmi" font-size="10">. </tspan>By the Theorem of
Pythagoras we have cos<tspan baseline-shift="sub"><tspan font-family="cmr" font-size="7">2</tspan></tspan><tspan font-family="cmmi" font-size="10"><img 
src="cmmi10-b.png" alt="a" class="10x-x-b" /></tspan>+sin<tspan baseline-shift="sub"><tspan font-family="cmr" font-size="7">2</tspan></tspan><tspan font-family="cmmi" font-size="10"><img 
src="cmmi10-b.png" alt="a" class="10x-x-b" /></tspan> = 1.
Thus the length of the blue line,
which is the cosine of <tspan font-family="cmmi" font-size="10"><img 
src="cmmi10-b.png" alt="a" class="10x-x-b" /></tspan>, must be
cos<tspan font-family="cmmi" font-size="10"><img 
src="cmmi10-b.png" alt="a" class="10x-x-b" /></tspan> = <img 
src="pgfmanual4x.gif" alt=" V~ 1---1/4-"  class="sqrt" > = <img 
src="pgfmanual5x.gif" alt="1
2"  class="frac" align="middle"><img 
src="pgfmanual6x.gif" alt=" V~ 3"  class="sqrt" ><tspan font-family="cmmi" font-size="10">.</tspan>This shows
that tan<tspan font-family="cmmi" font-size="10"><img 
src="cmmi10-b.png" alt="a" class="10x-x-b" /></tspan>, which is the height of the
orange line, is tan<tspan font-family="cmmi" font-size="10"><img 
src="cmmi10-b.png" alt="a" class="10x-x-b" /></tspan> = <img 
src="pgfmanual7x.gif" alt="sina-
cosa"  class="frac" align="middle"> = 1<tspan font-family="cmmi" font-size="10">/</tspan><img 
src="pgfmanual8x.gif" alt=" V~ 3"  class="sqrt" ><tspan font-family="cmmi" font-size="10">.</tspan></text> 
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