<PRE><B>Question 863135</B>
How do I find the cos(5pi/12)?! The question says &quot;Use the sum or difference formula to determine the value of the trigonometric function&quot;
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cos(5&amp;#960;/12)=cos(2&amp;#960;/12+3&amp;#960;/12)=cos(&amp;#960;/6+&amp;#960;/4)
Identity: cos(x+y)=cosxcosy-sinxsiny)
cosx=cos(&amp;#960;/6)=&amp;#8730;3/2
cosy=cos(&amp;#960;/4)=&amp;#8730;2/2
sinx=sin(&amp;#960;/6)=1/2
siny=sin(&amp;#960;/4)=&amp;#8730;2/2
cos(x+y)=&amp;#8730;3/2*&amp;#8730;2/2-1/2*&amp;#8730;2/2=&amp;#8730;6/4-&amp;#8730;2/4=(&amp;#8730;6-&amp;#8730;2)/4
...
calculator check:
cos(5&amp;#960;/12)&amp;#8776;0.2588…
exact value=(&amp;#8730;6-&amp;#8730;2)/4&amp;#8776;0.2588…</PRE>