document.write( "Question 285662: How do I find the exact ratio of sec pi/6? \n" ); document.write( "
Algebra.Com's Answer #207072 by nerdybill(7384)\"\" \"About 
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How do I find the exact ratio of sec pi/6?
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\n" ); document.write( "You find the exact value by applying identities and the \"unit circle\".
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\n" ); document.write( "From identities:
\n" ); document.write( "sec(pi/6) = 1/cos(pi/6)
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\n" ); document.write( "But, from the unit circle we know that cos(pi/6) is sqrt(3)/2
\n" ); document.write( "therefore:
\n" ); document.write( "sec(pi/6) = 1/cos(pi/6)
\n" ); document.write( "sec(pi/6) = 1/[sqrt(3)/2]
\n" ); document.write( "sec(pi/6) = 2/sqrt(3)
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\n" ); document.write( "Now we \"rationalize\" (remove sqrt from denominator):
\n" ); document.write( "sec(pi/6) = 2/sqrt(3) * sqrt(3)/sqrt(3)
\n" ); document.write( "sec(pi/6) = 2sqrt(3)/3 (this is your exact value)\r
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