document.write( "Question 820967: Find the exact value of cos n/4 \n" ); document.write( "
Algebra.Com's Answer #493867 by KMST(5328)\"\" \"About 
You can put this solution on YOUR website!
Maybe you meant \"cos%28pi%2F4%29\" .
\n" ); document.write( "The whole circle, \"360%5Eo\" is \"2pi\" measured in radians,
\n" ); document.write( "so \"pi%2F2\" is \"90%5Eo\" , a right angle.
\n" ); document.write( "A square has 4 congruent sides (equal length) and 4 right angles.
\n" ); document.write( "A diagonal divides a square into two isosceles right triangles,
\n" ); document.write( "with a right angle ( \"90%5Eo\" otr \"oi%2F2\" ,
\n" ); document.write( "and two congruent (equal measure) angles,
\n" ); document.write( "measuring \"45%5Eo\" or \"pi%2F4\" .
\n" ); document.write( "The trigonometric functions of such an angle can be calculated as the ratios of the sides of such a triangle.
\n" ); document.write( "If I make the length of the sides of my square \"1\" unit (of whatever unit you want), how long is that diagonal
\n" ); document.write( " The diagonal is the hypotenuse of a right triangle with legs measuring \"1\" .
\n" ); document.write( "The length of the diagonal is \"sqrt%281%5E2%2B1%5E2%29=sqrt%281%2B1%29=sqrt%282%29\" .
\n" ); document.write( "The sine of one of those \"pi%2F4\" angles is the ratio of opposite leg, divided by hypotenuse, so
\n" ); document.write( "\"sin%28pi%2F4%29=1%2Fsqrt%282%29\"
\n" ); document.write( "However, we do not like to see square roots in denominators, so we multiply numerator and denominator times \"sqrt%282%29\".
\n" ); document.write( "\"sin%28pi%2F4%29=sqrt%282%29%2F%28sqrt%282%29%2Asqrt%282%29%29\"
\n" ); document.write( "\"sin%28pi%2F4%29=sqrt%282%29%2F2\" \n" ); document.write( "
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