document.write( "Question 727492: Find the exact value of the expression sin^-1(tan 5pi/4)
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Algebra.Com's Answer #445239 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"5pi%2F4=pi%2Bpi%2F4\"$ and since tangent has a period of $\"pi\"$
\n" ); document.write( " $\"tan%285pi%2F4%29=tan%28pi%2F4%29\"$
\n" ); document.write( " $\"pi%2F4\"$ (in radians) is $\"45%5Eo\"$ , half of a right angle.
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\n" ); document.write( "You should know (or quickly figure out)
\n" ); document.write( "sine, cosine, and tangent of $\"30%5Eo\"$ , $\"45%5Eo\"$ and $\"60%5Eo\"$ ,
\n" ); document.write( "because a right triangle with $\"30%5Eo\"$ and $\"60%5Eo\"$ angles is half of an equilateral triangle,
\n" ); document.write( "and a right triangle with two $\"45%5Eo\"$ angles (an isosceles right triangle) is half of a square.
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$\"tan%2845%5Eo%29=a%2Fa=1\"$ and $\"sin%2845%5Eo%29=cos%2845%5Eo%29=a%2F%28sqrt%282%29a%29=1%2Fsqrt%282%29=sqrt%282%29%2F2\"$
\n" ); document.write( "So $\"tan%285pi%2F4%29=tan%28pi%2F4%29=tan%2845%5Eo%29=1\"$
\n" ); document.write( "and you should know that $\"sin%28pi%2F2%29=sin%2890%5Eo%29=1\"$
\n" ); document.write( "The angle between 0 and $\"pi\"$ $\"%28180%5Eo%29\"$ with a sine of 1 is $\"highlight%28pi%2F2%29\"$ and that is sin^-1(tan(5pi/4)) \n" ); document.write( "

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